audio
audioduration (s) 0.83
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stringlengths 3
127
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stringlengths 7
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x is plus or minus 1
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$x={}(\pm1)$
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https://www.youtube.com/watch?v=eRCN3daFCmU
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f of x is three x minus x cubed
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$f(x)=3x-x^{3}$
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https://www.youtube.com/watch?v=eRCN3daFCmU
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one over x plus two the quantity squared.
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$\frac{1}{({x+2})^2}$
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https://www.youtube.com/watch?v=twzGBqPeW0M
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negative two plus one
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$\-2 + 1\$
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https://www.youtube.com/watch?v=twzGBqPeW0M
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1 plus 1 over x
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$1+\frac{1}{x}$
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https://www.youtube.com/watch?v=twzGBqPeW0M
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1 plus 2 over x
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$1+\frac{2}{x}$
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https://www.youtube.com/watch?v=twzGBqPeW0M
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one minus one over x plus 2
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$1-\frac{1}{x+2}$
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https://www.youtube.com/watch?v=twzGBqPeW0M
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one times log x minus x times the derivative of log x
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$1\cdot\log x-x\cdot\frac{\mathrm{d}}{\mathrm{dx}}\log (x)$
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https://www.youtube.com/watch?v=twzGBqPeW0M
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log x minus one divided by log x squared
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$(\log (x)-1)/\log x^{2}$
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https://www.youtube.com/watch?v=twzGBqPeW0M
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e divided by log e
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$e/\log e$
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https://www.youtube.com/watch?v=twzGBqPeW0M
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log e is 1
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$\log(e) = {1}$
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https://www.youtube.com/watch?v=twzGBqPeW0M
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log x minus 1 divided by log x squared
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$\log(x-1)/(\log x)^{2}$
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https://www.youtube.com/watch?v=twzGBqPeW0M
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1 over log x minus 1 over log x squared
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$1/\log x - 1/(\log x^{2})$
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https://www.youtube.com/watch?v=twzGBqPeW0M
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1 over log 0 plus minus 1 over log 0 plus squared
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$\displaystyle \frac{1}{\log(0^{+})}-\frac{1}{(\log(0^{+}))^{2}}$
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https://www.youtube.com/watch?v=twzGBqPeW0M
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one over minus infinity minus 1 over infinity
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$\frac{1}{-\infty}-\frac{1}{\infty}$
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https://www.youtube.com/watch?v=twzGBqPeW0M
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minus log x to the minus 2 times 1 over x plus 2 log x to the minus 3 1 over x
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$\displaystyle -(\log x)^{-2} \cdot\frac{1}{x}+2(\log x)^{-3}\frac{1}{x}$
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https://www.youtube.com/watch?v=twzGBqPeW0M
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x log x cubed
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$x(\log x)^3$
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https://www.youtube.com/watch?v=twzGBqPeW0M
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2 minus log x
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$2-\log x$
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https://www.youtube.com/watch?v=twzGBqPeW0M
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e squared over two
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$\frac{e^{2}}{2}$
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https://www.youtube.com/watch?v=twzGBqPeW0M
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one minus x
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$\displaystyle 1-x$
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https://www.youtube.com/watch?v=YN7k_bXXggY
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x over 4
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$\frac{x}{4}$
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https://www.youtube.com/watch?v=YN7k_bXXggY
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x squared over 16
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$x^{2}/16$
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https://www.youtube.com/watch?v=YN7k_bXXggY
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the derivative of 1 minus x squared is 2 times 1 minus x times of minus 1
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$\displaystyle \frac{d}{dx}\left(1-x\right)^{2}=2\left(1-x\right)(-1)$
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https://www.youtube.com/watch?v=YN7k_bXXggY
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2x over 8
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$\frac{2x}{8}$
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https://www.youtube.com/watch?v=YN7k_bXXggY
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y is equal to v divided by x squared
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$y=\frac{v}{x^{2}}$
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https://www.youtube.com/watch?v=YN7k_bXXggY
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A prime is 2x minus 4v over x squared
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$A^{\prime}=2x-4v/x^{2}$
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https://www.youtube.com/watch?v=YN7k_bXXggY
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2x equals 2v over x squared
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$2x=2v/x^{2}$
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https://www.youtube.com/watch?v=YN7k_bXXggY
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x cubed is equal to 2v
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$x^{3}=2v$
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https://www.youtube.com/watch?v=YN7k_bXXggY
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x is equal to 2 to the 1 3rd v to the 1 3rd
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$x=2^{\frac{1}{3}}v^{\frac{1}{3}}$
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https://www.youtube.com/watch?v=YN7k_bXXggY
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x squared plus 4v over x
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$x^{2}+\frac{4v}{x}$
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https://www.youtube.com/watch?v=YN7k_bXXggY
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2x minus 4v over x squared
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$\displaystyle 2x-\frac{4v}{x^{2}}$
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https://www.youtube.com/watch?v=YN7k_bXXggY
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x squared plus 4v over x
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$x^{2}+4v/x$
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https://www.youtube.com/watch?v=YN7k_bXXggY
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two to the one third v to the one third squared plus four v
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$({2^{(1/3)}v^{(1/3)}})^{2}+4v$
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https://www.youtube.com/watch?v=YN7k_bXXggY
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a divided by v to the 2 3rds
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$\frac{a}{v^{2/3}}$
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https://www.youtube.com/watch?v=YN7k_bXXggY
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2 to the 1 3rd v to the 1 3rd divided by 2 to the minus 2 3rds v to the 1 3rd
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$2^{1/3}v^{1/3}\over 2^{-2/3}v^{1/3}$
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https://www.youtube.com/watch?v=YN7k_bXXggY
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2xy
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$(2xy)$
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https://www.youtube.com/watch?v=YN7k_bXXggY
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y prime is equal to minus 2xy divided by x squared
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$y^{\prime}=-\frac{2xy}{x^{2}}$
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https://www.youtube.com/watch?v=YN7k_bXXggY
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2x plus 4y plus 4x y prime
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$2x+4y+4xy^{\prime}$
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https://www.youtube.com/watch?v=YN7k_bXXggY
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4x times minus 2y over x
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$4x\cdot-\frac{2y}{x}$
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https://www.youtube.com/watch?v=YN7k_bXXggY
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2x plus 4y
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$\displaystyle 2x+4y$
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https://www.youtube.com/watch?v=YN7k_bXXggY
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8 minus 8y equals 0
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$8-8y=0.$
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https://www.youtube.com/watch?v=YN7k_bXXggY
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x over y is equal to 2
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$\frac{x}{y}=2$
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https://www.youtube.com/watch?v=YN7k_bXXggY
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x squared plus 30 squared is equal to d squared
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$x^{2}+30^{2}=d^{2}$
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https://www.youtube.com/watch?v=sRIDVAcoG5A
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d D dt is minus 80
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$\frac{\mathrm{d}}{\mathrm{d}t}D=-80$
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https://www.youtube.com/watch?v=sRIDVAcoG5A
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r divided by h is equal to four divided by ten
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$r/h=4/10$
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https://www.youtube.com/watch?v=sRIDVAcoG5A
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dv dt is two
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$\frac{dv}{dt} = 2$
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https://www.youtube.com/watch?v=sRIDVAcoG5A
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two fifths h
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$\frac{2}{5}h$
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https://www.youtube.com/watch?v=sRIDVAcoG5A
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v is equal to a 3rd pi times 2 5ths
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$v=\frac{1}{3}\pi\times\frac{2}{5}$
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https://www.youtube.com/watch?v=sRIDVAcoG5A
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h squared times h
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$\mathbb{h}^{2}\times\mathbb{h}$
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https://www.youtube.com/watch?v=sRIDVAcoG5A
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h squared times h
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$\mathbb{h}^{2}\times\mathbb{h}$
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https://www.youtube.com/watch?v=sRIDVAcoG5A
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3h squared times dh dt
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$\displaystyle 3h^{2}\frac{dh}{dt}$
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https://www.youtube.com/watch?v=sRIDVAcoG5A
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2 is equal to pi over 3 times 2 5ths
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$2=\frac{\pi}{3}\times\frac{2}{5}$
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https://www.youtube.com/watch?v=sRIDVAcoG5A
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dh dt is equal to 1 over 2pi
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$\frac{dh}{dt}=\frac{1}{2\pi}$
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https://www.youtube.com/watch?v=sRIDVAcoG5A
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dv dt is equal to dv dh times dh dt
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$dv/dt = \frac{dv}{dh}\times\frac{dh}{dt}$
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https://www.youtube.com/watch?v=sRIDVAcoG5A
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the square root of x squared plus y squared
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$\sqrt{x^{2}+y^{2}}$
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https://www.youtube.com/watch?v=sRIDVAcoG5A
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b minus y
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$\mathcal{b}{-}y$
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https://www.youtube.com/watch?v=sRIDVAcoG5A
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the square root of a minus x squared plus b minus y squared
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$\sqrt{(a-x)^{2}+(b-y)^{2}}$
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https://www.youtube.com/watch?v=sRIDVAcoG5A
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a minus x
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$\mathcal{a}-x$
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https://www.youtube.com/watch?v=sRIDVAcoG5A
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b minus y times y prime
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$(b - y)y^{\prime}$
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https://www.youtube.com/watch?v=sRIDVAcoG5A
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x divided by square root of x squared plus y squared
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$x/\sqrt{x^{2}+y^{2}}$
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https://www.youtube.com/watch?v=sRIDVAcoG5A
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x squared equals 5
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$\displaystyle x^{2}=5$
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https://www.youtube.com/watch?v=sRIDVAcoG5A
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f of x equal to x squared minus 5
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$f(x)=x^{2}-5$
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https://www.youtube.com/watch?v=sRIDVAcoG5A
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f of x equals 0
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$f(\mathbf{x})=0$
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https://www.youtube.com/watch?v=sRIDVAcoG5A
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y minus y0 is equal to m x minus x0
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$y-y_{0}=m(x-x_{0})$
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https://www.youtube.com/watch?v=sRIDVAcoG5A
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x1 is equal to x0 minus y0 divided by m
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$x_{1}=x_{0}-\frac{y_{0}}{m}$
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https://www.youtube.com/watch?v=sRIDVAcoG5A
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x0 is equal to 2
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$x_0 = 2$
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https://www.youtube.com/watch?v=sRIDVAcoG5A
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x0 squared minus 5
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$x_0^{2} - 5$
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https://www.youtube.com/watch?v=sRIDVAcoG5A
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minus a half x zero
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$-\frac{1}{2}x_{0}$
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https://www.youtube.com/watch?v=sRIDVAcoG5A
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five halves over x zero
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$\frac{5}{2}\over x_0$
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https://www.youtube.com/watch?v=sRIDVAcoG5A
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x one is a half times two
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$\displaystyle \mathbb{x}_{1}=\frac{1}{2}\times 2$
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https://www.youtube.com/watch?v=sRIDVAcoG5A
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9 4ths plus 5 halves times 4 9ths
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$(9/4+5/2)\times(4/9)$
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https://www.youtube.com/watch?v=sRIDVAcoG5A
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square root of 5 minus xn
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$\sqrt{5}-x_n$
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https://www.youtube.com/watch?v=sRIDVAcoG5A
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one minus a half
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$1-\frac{1}{2}$
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https://www.youtube.com/watch?v=sRIDVAcoG5A
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x minus x1 in absolute value
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$|x-x_1|$
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https://www.youtube.com/watch?v=4Q37iOyBq44
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e2 would be x minus x2 in absolute value
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$\displaystyle \mathbb{e}_2 = |x - x_{2}|$
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https://www.youtube.com/watch?v=4Q37iOyBq44
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y equals x squared minus 5
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$y=x^{2}-5$
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https://www.youtube.com/watch?v=4Q37iOyBq44
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the interval a less than x less than b
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$[a<x<b]$
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https://www.youtube.com/watch?v=4Q37iOyBq44
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f of b minus f of a divided by b minus a
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$(f(b)-f(a))/(b-a)$
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https://www.youtube.com/watch?v=4Q37iOyBq44
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f of b minus f of a over b minus a is equal to f prime of c
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$ \frac{f(b)-f(a)}{b-a}=f^{\prime}(c) $
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https://www.youtube.com/watch?v=4Q37iOyBq44
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f of b is equal to f of a plus f prime of c times b minus a
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$f(b)=f(a)+f^{\prime}(c)(b - a)$
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https://www.youtube.com/watch?v=4Q37iOyBq44
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e to the x minus 1 plus x
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$e^{x}-1+x$
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https://www.youtube.com/watch?v=4Q37iOyBq44
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e to the 0 minus 1 plus 0
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$(e^{0}-1)+0$
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https://www.youtube.com/watch?v=4Q37iOyBq44
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f prime of x is e to the x
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$f^{\prime}(x)=e^{x}$
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https://www.youtube.com/watch?v=4Q37iOyBq44
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e to the x is bigger than 1 plus x plus x squared over 2
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$e^{x}>(1+x+\frac{x^{2}}{2})$
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https://www.youtube.com/watch?v=4Q37iOyBq44
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x squared over 2
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$\frac{x^{2}}{2}$
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https://www.youtube.com/watch?v=4Q37iOyBq44
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x cubed over 3 times 2
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$\frac{x^{3}}{3\times 2}$
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https://www.youtube.com/watch?v=4Q37iOyBq44
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x to the fourth over four times three times two
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$x^{4}\over{4\times3\times2}$
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https://www.youtube.com/watch?v=4Q37iOyBq44
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x to the 1 3rd
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$x^{\frac{1}{3}}$
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https://www.youtube.com/watch?v=-MI0b4h3rS0
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one-third x to the minus two thirds
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$\frac{1}{3}x^{-\frac{2}{3}}$
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https://www.youtube.com/watch?v=-MI0b4h3rS0
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y is equal to 64 to the 1 3rd
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$y\mathrel{\mathop{=}}64^{1/3}$
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https://www.youtube.com/watch?v=-MI0b4h3rS0
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dy is 1 3rd times 64 to the minus 2 3rds dx
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$dy=\frac{1}{3}64^{-\frac{2}{3}}dx$
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https://www.youtube.com/watch?v=-MI0b4h3rS0
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dy is equal to 1 48th dx
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$dy=\frac{1}{48}dx$
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https://www.youtube.com/watch?v=-MI0b4h3rS0
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f prime of a times x minus a
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$f^{\prime}(a)(x-a)$
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https://www.youtube.com/watch?v=-MI0b4h3rS0
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f of x is x to the 1 3rd
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$f(x)=x^{1/3}$
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https://www.youtube.com/watch?v=-MI0b4h3rS0
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4 plus 1 over 48 times x minus a
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$(4+\frac{1}{48}(x-a))$
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https://www.youtube.com/watch?v=-MI0b4h3rS0
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one over a plus one
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$\frac{1}{a+1}$
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https://www.youtube.com/watch?v=-MI0b4h3rS0
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1 over negative x times the derivative with respect to x of negative x
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$\displaystyle \frac{1}{-x}\frac{d}{dx}(-x)$
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https://www.youtube.com/watch?v=-MI0b4h3rS0
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integral of secant squared x dx
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$\int \sec^{2}xdx$
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https://www.youtube.com/watch?v=-MI0b4h3rS0
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sine inverse x
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$\sin^{-1}x$
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https://www.youtube.com/watch?v=-MI0b4h3rS0
|
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the integral of dx over 1 plus x squared
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$\int\frac{dx}{1+x^{2}}$
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https://www.youtube.com/watch?v=-MI0b4h3rS0
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