1What is the formula for the differentiation quotient rule?
$\frac{d}{dx} \left( \frac{f}{g} \right) = \frac{g f' - f g'}{g^2}$
2$\text{What is } \frac{dy}{dx} \text{ for } y = f(u) \text{ and } u = g(x)?$
$\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}$
3$\text{How would you implicitly differentiate } y^4 + 3y - 4x^3 = 5x + 1 \, ?$
$4y^3 \frac{dy}{dx} + 3 \frac{dy}{dx} - 12x^2 = 5$
4$\frac{d}{dx} f^n$
$n f^{n-1} f'$
5$\frac{d}{dx} \ln(f)$
$\frac{f'}{f}$
6$\frac{d}{dx} \sin(f)$
$f' \cos(f)$
7$\frac{d}{dx} \cos(f)$
$-f' \sin(f)$
8$\frac{d}{dx} \tan(f)$
$f' \sec^2(f)$
9$\frac{d}{dx} \ln[\cos(f)]$
$-f' \tan(f)$
10$\frac{d}{dx} \arcsin(f)$
$\frac{f'}{\sqrt{1 - f^2}}$
11$\frac{d}{dx} \arccos(f)$
$\frac{-f'}{\sqrt{1 - f^2}}$
12$\frac{d}{dx} \arctan(f)$
$\frac{f'}{1 + f^2}$
13$\frac{d}{dx} \sinh(f)$
$f' \cosh(f)$
14$\frac{d}{dx} \cosh(f)$
$f' \sinh(f)$
15$\frac{d}{dx} \tanh(f)$
$f' \, \text{sech}^2(f)$
16$\frac{d}{dx} \text{arsinh}(f)$
$\frac{f'}{\sqrt{1 + f^2}}$
17$\frac{d}{dx} \text{arcosh}(f)$
$\frac{f'}{\sqrt{f^2 - 1}}$
18$\frac{d}{dx} \text{artanh}(f)$
$\frac{f'}{1 - f^2}$
19$\frac{d}{dx} c^f$
$f' c^f \ln(c)$
20$\frac{d}{dx} \log_c(f)$
$\frac{f'}{f \ln(c)}$
21$\frac{d}{dx} e^f$
$f' e^f$