Free Printable differentiation

1.

$\frac{\text{d}}{\text{d}x}\left(e^x\right)$

a)

$e^x$

b)

$-e^x$

c)

$\frac{1}{e^x}$

d)

$-\frac{1}{e^x}$

2.

Differentiate y = ln (5x - 7)

a)

_ 5 _

5x-7

b)

_ 1 _

5x-7

c)

ln5

d)

ln5x - ln 7

3.

Find the derivative of f(x) = 5x² + 7x - 3.

a)

2x + 7

b)

10x + 7

c)

10x + 4

d)

2x + 4

4.

If a function has a derivative that is negative, what does that tell you?

a)

The function is increasing

b)

The function is decreasing

5.

When do you use the chain rule?

a)

anytime you want

b)

when there is a function in a function

c)

where there are multiple layers to a lasagna (yum)

d)

when there is division

6.

Derivative means the same thing as

a)

slope of the tangent line

b)

slope of the normal line

c)

exponent

d)

potato

7.

How do you find horizontal tangent lines?

a)

Find where the derivative is undefined

b)

Find where the derivative equals zero

c)

Find where the derivative is 1

d)

Find where the derivative is negative

8.

What rule should be used in deriving h(x) = 2(x - 4)³

a)

Power rule

b)

Product rule

c)

Quotient rule

d)

Chain rule

9.

Which one is the product rule?

a)

f(x)g(x)

b)

f'(x)g(x)-f(x)g'(x)

c)

f'(x)g(x)+f(x)g'(x)

d)

f'(x)g'(x)+f'(x)g'(x)

10.

All the equations was TRUE accept...

a)

$\frac{\text{d}y}{\text{d}x}=\frac{\text{d}y}{\text{d}t}\times\frac{\text{d}t}{\text{d}x}$

b)

$\frac{\text{d}V}{\text{d}t}=\frac{\text{d}V}{\text{d}x}\times\frac{\text{d}x}{\text{d}t}$

c)

$\frac{\text{d}A}{\text{d}x}=\frac{\text{d}x}{\text{d}A}\times\frac{\text{d}A}{\text{d}t}$

d)

$\frac{\text{dA}}{\text{d}t}=\frac{\text{d}A}{\text{d}x}\times\frac{\text{d}x}{\text{d}t}$

11.

Stationary point occur when....

a)

x = 0

b)

$\frac{\text{d}y}{\text{d}x}=0$

c)

$\frac{\text{d}x}{\text{d}y}=0$

d)

$\frac{d^2y}{dx^2}=0$

12.

Match the following

a)

$\frac{d\left(\sin x\right)}{dx}$

1.

$\cos x$

b)

$\frac{d\left(\cos x\right)}{dx}$

2.

$-\sin x$

c)

$\frac{d\left(\tan x\right)}{dx}$

3.

$\sec^2x$

d)

$\frac{d\left(\sec x\right)}{dx}$

4.

$\sec x\tan x$

e)

$\frac{d\left(\operatorname{cosec}x\right)}{dx}$

5.

$-\operatorname{cosec}x\cot x$

13.

What is the derivative of cot(x)?

a)

sec²(x)

b)

-sec²(x)

c)

csc²(x)

d)

-csc²(x)

14.

Find the derivative.

a)

x⁴cosx - 4x³sinx

b)

x⁴cosx + 4x³sinx

c)

4x³cosx

d)

-4x³cosx

15.

What is the derivative of xⁿ?

a)

(n-1)xⁿ

b)

nxⁿ⁺¹

c)

(n+1)x^n-1

d)

nx^n-1

differentiation

Total questions: 15

Worksheet time: 8mins

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