Free Printable Derivative Rules

1.

$\frac{d}{dx}\left[\sin u\right]$

a)

$\cos u\cdot du$

b)

$-\cos u\cdot du$

c)

$\cos x$

d)

$-\cos x$

2.

$\frac{d}{dx}\left[\cos u\right]$

a)

$\sin u\cdot du$

b)

$-\sin u\cdot du$

c)

$-\sin\ x$

d)

$\sin\ x$

3.

$\frac{d}{dx}\left[x^n\right]$

a)

$n\cdot x^n$

b)

$\frac{1}{n}\cdot x^{n+1}$

c)

$n\cdot x^{n-1}$

d)

$\frac{1}{n}\cdot x^{n-1}$

4.

$\frac{d}{dx}\left[\tan u\right]$

a)

$\sec^2u\cdot du$

b)

$\sec u\tan u\cdot du$

c)

$-\csc u\cot u\cdot du$

d)

$-\csc^2u\cdot du$

5.

$\frac{d}{dx}\left[\cot u\right]$

a)

$-\sec^2u\cdot du$

b)

$-\csc^2u\cdot du$

c)

$-\csc u\cot u\cdot du$

d)

$-\sec u\tan u\cdot du$

6.

$\frac{d}{dx}\left[\sec u\right]$

a)

$\csc^2u\cdot du$

b)

$\sec u\tan u\cdot du$

c)

$\csc u\cot u\cdot du$

d)

$\sec^2u\cdot du$

7.

$\frac{d}{dx}\left[\csc u\right]$

a)

$-\sec^2u\cdot du$

b)

$-\csc^2u\cdot du$

c)

$-\sec u\tan u\cdot du$

d)

$-\csc u\cot u\cdot du$

8.

$\frac{d}{dx}\left[f\left(x\right)\cdot g\left(x\right)\right]$

a)

$f'\left(x\right)\cdot g'\left(x\right)$

b)

$f'\left(x\right)\cdot g\left(x\right)-g'\left(x\right)\cdot f\left(x\right)$

c)

$f'\left(g\left(x\right)\right)\cdot g'\left(x\right)$

d)

$f\left(x\right)\cdot g'\left(x\right)+f'\left(x\right)\cdot g\left(x\right)$

9.

$\frac{d}{dx}\left[\frac{f}{g}\right]$

a)

$g\cdot f'-f\cdot g'$

b)

$\frac{g\cdot f'-f\cdot g'}{g^2}$

c)

$\frac{f'\cdot g-g'\cdot f}{g^2}$

d)

$\frac{f'}{g'}$

10.

$\frac{d}{dx}\left[a^u\right]$

a)

$\left(\ln\ a\right)a^u$

b)

$\frac{1}{\ln\ a}a^u\cdot du$

c)

$\frac{1}{\ln\ a}\cdot\frac{1}{u}\cdot du$

d)

$\left(\ln a\right)a^u\cdot du$

11.

$\frac{d}{dx}\left[\log_au\right]$

a)

$\left(\ln\ a\right)\log_au\cdot du$

b)

$\frac{1}{\ln\ a}a^u\cdot du$

c)

$\frac{1}{\ln\ a}\cdot\frac{1}{u}\cdot du$

d)

$\left(\ln a\right)\cdot\frac{du}{u}$

12.

$\frac{d}{dx}\left[e^u\right]$

a)

$\frac{1}{\ln\ e^u}\cdot du$

b)

$e^u\cdot du$

c)

$\ln\ e^u\cdot du$

d)

$e^u$

13.

$\frac{d}{dx}\left[\ln u\right]$

a)

$\frac{1}{u}\cdot du$

b)

$\frac{1}{x}$

c)

$\ln e^u$

d)

$\frac{1}{\ln u}\cdot du$

14.

$\frac{d}{dx}\left[f\left(u\right)\right]$

a)

$f'\left(u\right)\cdot f\left(u\right)\cdot du$

b)

$f'\left(u\right)$

c)

$f'\left(du\right)$

d)

$f'\left(u\right)\cdot du$

15.

$\frac{d}{dx}\left[\arcsin u\right]$

a)

$\frac{1}{\sqrt{1-u^2}}\cdot du$

b)

$\frac{1}{\sqrt{u^2-1}}\cdot du$

c)

$\frac{-1}{\sqrt{1-u^2}}\cdot du$

d)

$\frac{1}{1+u^2}\cdot du$

16.

$\frac{d}{dx}\left[\arccos u\right]$

a)

$\frac{1}{\sqrt{1-u^2}}\cdot du$

b)

$\frac{-1}{\sqrt{u^2-1}}\cdot du$

c)

$\frac{-1}{\sqrt{1-u^2}}\cdot du$

d)

$\frac{1}{\sqrt{u^2-1}}\cdot du$

17.

$\frac{d}{dx}\left[\arctan u\right]$

a)

$\frac{-1}{u^2+1}\cdot du$

b)

$\frac{1}{u^2-1}\cdot du$

c)

$\frac{1}{1-u^2}\cdot du$

d)

$\frac{1}{1+u^2}\cdot du$

18.

$\frac{d}{dx}\left[\operatorname{arccot}u\right]$

a)

$\frac{-1}{\sqrt{1-u^2}}\cdot du$

b)

$\frac{-1}{\left|u\right|\sqrt{u^2-1}}\cdot du$

c)

$\frac{-1}{u^2+1}\cdot du$

d)

$\frac{1}{1+u^2}\cdot du$

19.

$\frac{d}{dx}\left[\operatorname{arccsc}u\right]$

a)

$\frac{-1}{\left|u\right|\sqrt{1-u^2}}\cdot du$

b)

$\frac{-1}{\left|u\right|\sqrt{u^2-1}}\cdot du$

c)

$\frac{-1}{u^2+1}\cdot du$

d)

$\frac{-1}{\sqrt{u^2-1}}\cdot du$

20.

$\frac{d}{dx}\left[\operatorname{arcsec}u\right]$

a)

$\frac{1}{\left|u\right|\sqrt{1-u^2}}\cdot du$

b)

$\frac{1}{\left|u\right|\sqrt{u^2-1}}\cdot du$

c)

$\frac{1}{u^2+1}\cdot du$

d)

$\frac{1}{\sqrt{u^2-1}}\cdot du$

21.

The derivative of the inverse of $f\left(x\right)$ given $g\left(x\right)=f^{-1}\left(x\right)$ is...

a)

$\frac{1}{f'\left(g\left(x\right)\right)}$

b)

$\frac{1}{f'\left(g^{-1}\left(x\right)\right)}$

c)

$f'\left(g\left(x\right)\right)$

d)

$\frac{1}{f\left(g'\left(x\right)\right)}$

Derivative Rules

Total questions: 21

Worksheet time: 11mins

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