Free Printable I.2. Common derivatives (Review of Derivatives)

1.

Find the derivative of $f\left(x\right)=c$ , where $c$ is a constant.

a)

$f'\left(x\right)=0$

b)

$f'\left(x\right)=c$

c)

$f'\left(x\right)=1$

d)

$f'\left(x\right)=cx$

2.

Find the derivative of $f\left(x\right)=x^n$ .

a)

$f'\left(x\right)=nx$

b)

$f'\left(x\right)=nx^{n+1}$

c)

$f'\left(x\right)=nx^{n-1}$

d)

$f'\left(x\right)=x^{n-1}$

3.

What is the derivative of $c\cdot f\left(x\right)$ , where $c$ is a constant?

a)

$0$

b)

$c$

c)

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

d)

$f'\left(x\right)$

4.

What is the derivative of the function $\left(f+g\right)\left(x\right)?$

a)

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

b)

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

c)

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

d)

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

5.

The product rule: What is the derivative of $\left(f\cdot g\right)\left(x\right)?$

a)

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

b)

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

6.

The quotient rule: What is the derivative of $\left(\frac{f}{g}\right)\left(x\right)?$

a)

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

b)

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

c)

$\frac{g\left(x\right)\cdot f'\left(x\right)-f\left(x\right)\cdot g'\left(x\right)}{\left(g\left(x\right)\right)^2}$

7.

In the questions above, what did we assume about the functions $f$ and $g?$

a)

They are both continuous

b)

They are both differentiable

c)

They are not equal

d)

Neither are constant functions

8.

What is the derivative of $f\left(x\right)=\sin\left(x\right)?$ Include the signs when answering.

a)

-

b)

+

c)

$\sin\left(x\right)$

d)

$\cos\left(x\right)$

e)

$\tan\left(x\right)$

9.

What is the derivative of $f\left(x\right)=\cos\left(x\right)?$ Include the signs when answering.

a)

-

b)

+

c)

$\sin\left(x\right)$

d)

$\cos\left(x\right)$

e)

$\sec\left(x\right)$

10.

What is the derivative of $f\left(x\right)=\tan\left(x\right)?$ Include the signs when answering.

a)

-

b)

+

c)

$\cot\left(x\right)$

d)

$\sec\left(x\right)$

e)

$\sec^2\left(x\right)$

11.

What is the derivative of $f\left(x\right)=\sec\left(x\right)?$ Include the signs when answering.

a)

-

b)

+

c)

$\sec\left(x\right)\cdot\tan\left(x\right)$

d)

$\text{}\csc\left(x\right)\cdot\cot\left(x\right)$

e)

$\tan^2\left(x\right)$

12.

What is the derivative of $f\left(x\right)=\csc\left(x\right)?$ Include the signs when answering.

a)

-

b)

+

c)

$\sec\left(x\right)\cdot\tan\left(x\right)$

d)

$\csc\left(x\right)\cdot\cot\left(x\right)$

e)

$\cot^2\left(x\right)$

13.

What is the derivative of $f\left(x\right)=\cot\left(x\right)?$ Include the signs when answering.

a)

-

b)

+

c)

$\tan\left(x\right)$

d)

$\csc\left(x\right)\cot\left(x\right)$

e)

$\csc^2\left(x\right)$

14.

What is the derivative of $f\left(x\right)=e^x?$

a)

$x\left(e^{x-1}\right)$

b)

$xe^x$

c)

$e^x$

d)

$e$

I.2. Common derivatives (Review of Derivatives)

Total questions: 14

Worksheet time: 6mins

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