Differentiation

Question 1

What is the formula for the differentiation quotient rule?

Accepted Answer

$\frac{d}{dx} \left( \frac{f}{g} \right) = \frac{g f' - f g'}{g^2}$

Question 2

$	ext{What is } \frac{dy}{dx} 	ext{ for } y = f(u) 	ext{ and } u = g(x)?$

Accepted Answer

$\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}$

Question 3

$	ext{How would you implicitly differentiate } y^4 + 3y - 4x^3 = 5x + 1 \, ?$

Accepted Answer

$4y^3 \frac{dy}{dx} + 3 \frac{dy}{dx} - 12x^2 = 5$

Question 4

$\frac{d}{dx} f^n$

Accepted Answer

$n f^{n-1} f'$

Question 5

$\frac{d}{dx} \ln(f)$

Accepted Answer

$\frac{f'}{f}$

Question 6

$\frac{d}{dx} \sin(f)$

Accepted Answer

$f' \cos(f)$

Question 7

$\frac{d}{dx} \cos(f)$

Accepted Answer

$-f' \sin(f)$

Question 8

$\frac{d}{dx} 	an(f)$

Accepted Answer

$f' \sec^2(f)$

Question 9

$\frac{d}{dx} \ln[\cos(f)]$

Accepted Answer

$-f' 	an(f)$

Question 10

$\frac{d}{dx} \arcsin(f)$

Accepted Answer

$\frac{f'}{\sqrt{1 - f^2}}$

Question 11

$\frac{d}{dx} \arccos(f)$

Accepted Answer

$\frac{-f'}{\sqrt{1 - f^2}}$

Question 12

$\frac{d}{dx} \arctan(f)$

Accepted Answer

$\frac{f'}{1 + f^2}$

Question 13

$\frac{d}{dx} \sinh(f)$

Accepted Answer

$f' \cosh(f)$

Question 14

$\frac{d}{dx} \cosh(f)$

Accepted Answer

$f' \sinh(f)$

Question 15

$\frac{d}{dx} 	anh(f)$

Accepted Answer

$f' \, 	ext{sech}^2(f)$

Question 16

$\frac{d}{dx} 	ext{arsinh}(f)$

Accepted Answer

$\frac{f'}{\sqrt{1 + f^2}}$

Question 17

$\frac{d}{dx} 	ext{arcosh}(f)$

Accepted Answer

$\frac{f'}{\sqrt{f^2 - 1}}$

Question 18

$\frac{d}{dx} 	ext{artanh}(f)$

Accepted Answer

$\frac{f'}{1 - f^2}$

Question 19

$\frac{d}{dx} c^f$

Accepted Answer

$f' c^f \ln(c)$

Question 20

$\frac{d}{dx} \log_c(f)$

Accepted Answer

$\frac{f'}{f \ln(c)}$

Question 21

$\frac{d}{dx} e^f$

Accepted Answer

$f' e^f$

Alle Karten