audio
audioduration (s) 0.83
21
| transcription
stringlengths 3
127
| LaTeX
stringlengths 7
142
| Source
stringclasses 89
values |
|---|---|---|---|
x is plus or minus 1 | $x={}(\pm1)$ | https://www.youtube.com/watch?v=eRCN3daFCmU |
|
f of x is three x minus x cubed | $f(x)=3x-x^{3}$ | https://www.youtube.com/watch?v=eRCN3daFCmU |
|
one over x plus two the quantity squared. | $\frac{1}{({x+2})^2}$ | https://www.youtube.com/watch?v=twzGBqPeW0M |
|
negative two plus one | $\-2 + 1\$ | https://www.youtube.com/watch?v=twzGBqPeW0M |
|
1 plus 1 over x | $1+\frac{1}{x}$ | https://www.youtube.com/watch?v=twzGBqPeW0M |
|
1 plus 2 over x | $1+\frac{2}{x}$ | https://www.youtube.com/watch?v=twzGBqPeW0M |
|
one minus one over x plus 2 | $1-\frac{1}{x+2}$ | https://www.youtube.com/watch?v=twzGBqPeW0M |
|
one times log x minus x times the derivative of log x | $1\cdot\log x-x\cdot\frac{\mathrm{d}}{\mathrm{dx}}\log (x)$ | https://www.youtube.com/watch?v=twzGBqPeW0M |
|
log x minus one divided by log x squared | $(\log (x)-1)/\log x^{2}$ | https://www.youtube.com/watch?v=twzGBqPeW0M |
|
e divided by log e | $e/\log e$ | https://www.youtube.com/watch?v=twzGBqPeW0M |
|
log e is 1 | $\log(e) = {1}$ | https://www.youtube.com/watch?v=twzGBqPeW0M |
|
log x minus 1 divided by log x squared | $\log(x-1)/(\log x)^{2}$ | https://www.youtube.com/watch?v=twzGBqPeW0M |
|
1 over log x minus 1 over log x squared | $1/\log x - 1/(\log x^{2})$ | https://www.youtube.com/watch?v=twzGBqPeW0M |
|
1 over log 0 plus minus 1 over log 0 plus squared | $\displaystyle \frac{1}{\log(0^{+})}-\frac{1}{(\log(0^{+}))^{2}}$ | https://www.youtube.com/watch?v=twzGBqPeW0M |
|
one over minus infinity minus 1 over infinity | $\frac{1}{-\infty}-\frac{1}{\infty}$ | https://www.youtube.com/watch?v=twzGBqPeW0M |
|
minus log x to the minus 2 times 1 over x plus 2 log x to the minus 3 1 over x | $\displaystyle -(\log x)^{-2} \cdot\frac{1}{x}+2(\log x)^{-3}\frac{1}{x}$ | https://www.youtube.com/watch?v=twzGBqPeW0M |
|
x log x cubed | $x(\log x)^3$ | https://www.youtube.com/watch?v=twzGBqPeW0M |
|
2 minus log x | $2-\log x$ | https://www.youtube.com/watch?v=twzGBqPeW0M |
|
e squared over two | $\frac{e^{2}}{2}$ | https://www.youtube.com/watch?v=twzGBqPeW0M |
|
one minus x | $\displaystyle 1-x$ | https://www.youtube.com/watch?v=YN7k_bXXggY |
|
x over 4 | $\frac{x}{4}$ | https://www.youtube.com/watch?v=YN7k_bXXggY |
|
x squared over 16 | $x^{2}/16$ | https://www.youtube.com/watch?v=YN7k_bXXggY |
|
the derivative of 1 minus x squared is 2 times 1 minus x times of minus 1 | $\displaystyle \frac{d}{dx}\left(1-x\right)^{2}=2\left(1-x\right)(-1)$ | https://www.youtube.com/watch?v=YN7k_bXXggY |
|
2x over 8 | $\frac{2x}{8}$ | https://www.youtube.com/watch?v=YN7k_bXXggY |
|
y is equal to v divided by x squared | $y=\frac{v}{x^{2}}$ | https://www.youtube.com/watch?v=YN7k_bXXggY |
|
A prime is 2x minus 4v over x squared | $A^{\prime}=2x-4v/x^{2}$ | https://www.youtube.com/watch?v=YN7k_bXXggY |
|
2x equals 2v over x squared | $2x=2v/x^{2}$ | https://www.youtube.com/watch?v=YN7k_bXXggY |
|
x cubed is equal to 2v | $x^{3}=2v$ | https://www.youtube.com/watch?v=YN7k_bXXggY |
|
x is equal to 2 to the 1 3rd v to the 1 3rd | $x=2^{\frac{1}{3}}v^{\frac{1}{3}}$ | https://www.youtube.com/watch?v=YN7k_bXXggY |
|
x squared plus 4v over x | $x^{2}+\frac{4v}{x}$ | https://www.youtube.com/watch?v=YN7k_bXXggY |
|
2x minus 4v over x squared | $\displaystyle 2x-\frac{4v}{x^{2}}$ | https://www.youtube.com/watch?v=YN7k_bXXggY |
|
x squared plus 4v over x | $x^{2}+4v/x$ | https://www.youtube.com/watch?v=YN7k_bXXggY |
|
two to the one third v to the one third squared plus four v | $({2^{(1/3)}v^{(1/3)}})^{2}+4v$ | https://www.youtube.com/watch?v=YN7k_bXXggY |
|
a divided by v to the 2 3rds | $\frac{a}{v^{2/3}}$ | https://www.youtube.com/watch?v=YN7k_bXXggY |
|
2 to the 1 3rd v to the 1 3rd divided by 2 to the minus 2 3rds v to the 1 3rd | $2^{1/3}v^{1/3}\over 2^{-2/3}v^{1/3}$ | https://www.youtube.com/watch?v=YN7k_bXXggY |
|
2xy | $(2xy)$ | https://www.youtube.com/watch?v=YN7k_bXXggY |
|
y prime is equal to minus 2xy divided by x squared | $y^{\prime}=-\frac{2xy}{x^{2}}$ | https://www.youtube.com/watch?v=YN7k_bXXggY |
|
2x plus 4y plus 4x y prime | $2x+4y+4xy^{\prime}$ | https://www.youtube.com/watch?v=YN7k_bXXggY |
|
4x times minus 2y over x | $4x\cdot-\frac{2y}{x}$ | https://www.youtube.com/watch?v=YN7k_bXXggY |
|
2x plus 4y | $\displaystyle 2x+4y$ | https://www.youtube.com/watch?v=YN7k_bXXggY |
|
8 minus 8y equals 0 | $8-8y=0.$ | https://www.youtube.com/watch?v=YN7k_bXXggY |
|
x over y is equal to 2 | $\frac{x}{y}=2$ | https://www.youtube.com/watch?v=YN7k_bXXggY |
|
x squared plus 30 squared is equal to d squared | $x^{2}+30^{2}=d^{2}$ | https://www.youtube.com/watch?v=sRIDVAcoG5A |
|
d D dt is minus 80 | $\frac{\mathrm{d}}{\mathrm{d}t}D=-80$ | https://www.youtube.com/watch?v=sRIDVAcoG5A |
|
r divided by h is equal to four divided by ten | $r/h=4/10$ | https://www.youtube.com/watch?v=sRIDVAcoG5A |
|
dv dt is two | $\frac{dv}{dt} = 2$ | https://www.youtube.com/watch?v=sRIDVAcoG5A |
|
two fifths h | $\frac{2}{5}h$ | https://www.youtube.com/watch?v=sRIDVAcoG5A |
|
v is equal to a 3rd pi times 2 5ths | $v=\frac{1}{3}\pi\times\frac{2}{5}$ | https://www.youtube.com/watch?v=sRIDVAcoG5A |
|
h squared times h | $\mathbb{h}^{2}\times\mathbb{h}$ | https://www.youtube.com/watch?v=sRIDVAcoG5A |
|
h squared times h | $\mathbb{h}^{2}\times\mathbb{h}$ | https://www.youtube.com/watch?v=sRIDVAcoG5A |
|
3h squared times dh dt | $\displaystyle 3h^{2}\frac{dh}{dt}$ | https://www.youtube.com/watch?v=sRIDVAcoG5A |
|
2 is equal to pi over 3 times 2 5ths | $2=\frac{\pi}{3}\times\frac{2}{5}$ | https://www.youtube.com/watch?v=sRIDVAcoG5A |
|
dh dt is equal to 1 over 2pi | $\frac{dh}{dt}=\frac{1}{2\pi}$ | https://www.youtube.com/watch?v=sRIDVAcoG5A |
|
dv dt is equal to dv dh times dh dt | $dv/dt = \frac{dv}{dh}\times\frac{dh}{dt}$ | https://www.youtube.com/watch?v=sRIDVAcoG5A |
|
the square root of x squared plus y squared | $\sqrt{x^{2}+y^{2}}$ | https://www.youtube.com/watch?v=sRIDVAcoG5A |
|
b minus y | $\mathcal{b}{-}y$ | https://www.youtube.com/watch?v=sRIDVAcoG5A |
|
the square root of a minus x squared plus b minus y squared | $\sqrt{(a-x)^{2}+(b-y)^{2}}$ | https://www.youtube.com/watch?v=sRIDVAcoG5A |
|
a minus x | $\mathcal{a}-x$ | https://www.youtube.com/watch?v=sRIDVAcoG5A |
|
b minus y times y prime | $(b - y)y^{\prime}$ | https://www.youtube.com/watch?v=sRIDVAcoG5A |
|
x divided by square root of x squared plus y squared | $x/\sqrt{x^{2}+y^{2}}$ | https://www.youtube.com/watch?v=sRIDVAcoG5A |
|
x squared equals 5 | $\displaystyle x^{2}=5$ | https://www.youtube.com/watch?v=sRIDVAcoG5A |
|
f of x equal to x squared minus 5 | $f(x)=x^{2}-5$ | https://www.youtube.com/watch?v=sRIDVAcoG5A |
|
f of x equals 0 | $f(\mathbf{x})=0$ | https://www.youtube.com/watch?v=sRIDVAcoG5A |
|
y minus y0 is equal to m x minus x0 | $y-y_{0}=m(x-x_{0})$ | https://www.youtube.com/watch?v=sRIDVAcoG5A |
|
x1 is equal to x0 minus y0 divided by m | $x_{1}=x_{0}-\frac{y_{0}}{m}$ | https://www.youtube.com/watch?v=sRIDVAcoG5A |
|
x0 is equal to 2 | $x_0 = 2$ | https://www.youtube.com/watch?v=sRIDVAcoG5A |
|
x0 squared minus 5 | $x_0^{2} - 5$ | https://www.youtube.com/watch?v=sRIDVAcoG5A |
|
minus a half x zero | $-\frac{1}{2}x_{0}$ | https://www.youtube.com/watch?v=sRIDVAcoG5A |
|
five halves over x zero | $\frac{5}{2}\over x_0$ | https://www.youtube.com/watch?v=sRIDVAcoG5A |
|
x one is a half times two | $\displaystyle \mathbb{x}_{1}=\frac{1}{2}\times 2$ | https://www.youtube.com/watch?v=sRIDVAcoG5A |
|
9 4ths plus 5 halves times 4 9ths | $(9/4+5/2)\times(4/9)$ | https://www.youtube.com/watch?v=sRIDVAcoG5A |
|
square root of 5 minus xn | $\sqrt{5}-x_n$ | https://www.youtube.com/watch?v=sRIDVAcoG5A |
|
one minus a half | $1-\frac{1}{2}$ | https://www.youtube.com/watch?v=sRIDVAcoG5A |
|
x minus x1 in absolute value | $|x-x_1|$ | https://www.youtube.com/watch?v=4Q37iOyBq44 |
|
e2 would be x minus x2 in absolute value | $\displaystyle \mathbb{e}_2 = |x - x_{2}|$ | https://www.youtube.com/watch?v=4Q37iOyBq44 |
|
y equals x squared minus 5 | $y=x^{2}-5$ | https://www.youtube.com/watch?v=4Q37iOyBq44 |
|
the interval a less than x less than b | $[a<x<b]$ | https://www.youtube.com/watch?v=4Q37iOyBq44 |
|
f of b minus f of a divided by b minus a | $(f(b)-f(a))/(b-a)$ | https://www.youtube.com/watch?v=4Q37iOyBq44 |
|
f of b minus f of a over b minus a is equal to f prime of c | $ \frac{f(b)-f(a)}{b-a}=f^{\prime}(c) $ | https://www.youtube.com/watch?v=4Q37iOyBq44 |
|
f of b is equal to f of a plus f prime of c times b minus a | $f(b)=f(a)+f^{\prime}(c)(b - a)$ | https://www.youtube.com/watch?v=4Q37iOyBq44 |
|
e to the x minus 1 plus x | $e^{x}-1+x$ | https://www.youtube.com/watch?v=4Q37iOyBq44 |
|
e to the 0 minus 1 plus 0 | $(e^{0}-1)+0$ | https://www.youtube.com/watch?v=4Q37iOyBq44 |
|
f prime of x is e to the x | $f^{\prime}(x)=e^{x}$ | https://www.youtube.com/watch?v=4Q37iOyBq44 |
|
e to the x is bigger than 1 plus x plus x squared over 2 | $e^{x}>(1+x+\frac{x^{2}}{2})$ | https://www.youtube.com/watch?v=4Q37iOyBq44 |
|
x squared over 2 | $\frac{x^{2}}{2}$ | https://www.youtube.com/watch?v=4Q37iOyBq44 |
|
x cubed over 3 times 2 | $\frac{x^{3}}{3\times 2}$ | https://www.youtube.com/watch?v=4Q37iOyBq44 |
|
x to the fourth over four times three times two | $x^{4}\over{4\times3\times2}$ | https://www.youtube.com/watch?v=4Q37iOyBq44 |
|
x to the 1 3rd | $x^{\frac{1}{3}}$ | https://www.youtube.com/watch?v=-MI0b4h3rS0 |
|
one-third x to the minus two thirds | $\frac{1}{3}x^{-\frac{2}{3}}$ | https://www.youtube.com/watch?v=-MI0b4h3rS0 |
|
y is equal to 64 to the 1 3rd | $y\mathrel{\mathop{=}}64^{1/3}$ | https://www.youtube.com/watch?v=-MI0b4h3rS0 |
|
dy is 1 3rd times 64 to the minus 2 3rds dx | $dy=\frac{1}{3}64^{-\frac{2}{3}}dx$ | https://www.youtube.com/watch?v=-MI0b4h3rS0 |
|
dy is equal to 1 48th dx | $dy=\frac{1}{48}dx$ | https://www.youtube.com/watch?v=-MI0b4h3rS0 |
|
f prime of a times x minus a | $f^{\prime}(a)(x-a)$ | https://www.youtube.com/watch?v=-MI0b4h3rS0 |
|
f of x is x to the 1 3rd | $f(x)=x^{1/3}$ | https://www.youtube.com/watch?v=-MI0b4h3rS0 |
|
4 plus 1 over 48 times x minus a | $(4+\frac{1}{48}(x-a))$ | https://www.youtube.com/watch?v=-MI0b4h3rS0 |
|
one over a plus one | $\frac{1}{a+1}$ | https://www.youtube.com/watch?v=-MI0b4h3rS0 |
|
1 over negative x times the derivative with respect to x of negative x | $\displaystyle \frac{1}{-x}\frac{d}{dx}(-x)$ | https://www.youtube.com/watch?v=-MI0b4h3rS0 |
|
integral of secant squared x dx | $\int \sec^{2}xdx$ | https://www.youtube.com/watch?v=-MI0b4h3rS0 |
|
sine inverse x | $\sin^{-1}x$ | https://www.youtube.com/watch?v=-MI0b4h3rS0 |
|
the integral of dx over 1 plus x squared | $\int\frac{dx}{1+x^{2}}$ | https://www.youtube.com/watch?v=-MI0b4h3rS0 |