Free Printable Revision on differentation

1.

Find the derivative of f(x) = 2x²+3.

a)

4x

b)

4x²

c)

3

d)

4x+3

2.

Differentiate y= 12x^-2

a)

24x^-1

b)

-24x^-3

c)

-24x^-1

d)

6x^-3

3.

Find the derivative of the given equation
f(x) = 7

a)

7

b)

0

c)

7x

d)

14

4.

Find the derivative of the given equation
f(x) = 1/x²

a)

1/2x

b)

-2x

c)

2x

d)

-2x^-3

5.

Derivative means the same thing as

a)

slope of the tangent line

b)

slope of the normal line

c)

exponent

d)

potato

6.

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

a)

The function is increasing

b)

The function is decreasing

7.

The derivative of a function is its

a)

Sign

b)

Maximum/Minimum

c)

Instantaneous rate of change

d)

Common Denominator

8.

Find the derivative of:
f(x) = 7(3x+ 4)⁵

a)

35(3x + 4)⁵

b)

35(3x + 4)⁴

c)

105(3x + 4)⁵

d)

105(3x + 4)⁴

9.

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

10.

What rule best apply to find the derivative of y=x lnx

a)

product rule

b)

quotient rule

c)

power rule

d)

sum rule

11.

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

a)

$e^x$

b)

$-e^x$

c)

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

d)

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

12.

Differentiate y = ln (5x - 7)

a)

_ 5 _

5x-7

b)

_ 1 _

5x-7

c)

ln5

d)

ln5x - ln 7

13.

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)

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

14.

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.

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

15.

What is the derivative of cot(x)?

a)

sec²(x)

b)

-sec²(x)

c)

csc²(x)

d)

-csc²(x)

16.

Find the derivative.

a)

x⁴cosx - 4x³sinx

b)

x⁴cosx + 4x³sinx

c)

4x³cosx

d)

-4x³cosx

17.

Find the derivative of
f(x) = (x⁶ + 4)⁵

a)

f '(x) = 5x⁵(x⁴ + 4)⁴

b)

f '(x) = 6x⁵(x⁶ + 4)⁴

c)

f '(x) = 30x⁵(x⁶ + 4)⁴

d)

f '(x) = 30x⁶(x⁶ + 4)⁴

18.

Which rule would you need to use?

a)

Power Rule

b)

Product Rule

c)

Quotient Rule

d)

Chain Rule

19.

Find the derivative of:
f(x) = (x²+1)⁶

a)

12(x² + 1)⁶

b)

12x(x² + 1)⁶

c)

12x(x² + 1)⁵

d)

12(x² + 1)⁵

20.

What is the "outer" part of the composite function:
$\sqrt{x^2+1}$

a)

$\sqrt{x}$

b)

$x^2+1$

c)

This is not a composite function

21.

What is the "inner" part of the composite function:
$\left(\sin x\right)^2$

a)

$x^2$

b)

$\sin x$

c)

This is not a composite function

22.

What is the "outer" part for this composite function:
$2\left(x^3-1\right)^2$

a)

$2x^2$

b)

$x^3-1$

c)

This is not a composite function.

23.

Find the derivative of following with respect to x:
$f\left(x\right)=\sqrt{\cos\left(x\right)}$

a)

f '(x) = $-\frac{\sin\left(x\right)}{2\cos^2\left(x\right)}$

b)

f '(x) = $\frac{2\sin\left(x\right)}{\sqrt{\cos\left(x\right)}}$

c)

f '(x) = $-\frac{\sin\left(x\right)}{2\sqrt{\cos\left(x\right)}}$

d)

f '(x) = $-\frac{\sin\left(x\right)}{\sqrt{\cos\left(x\right)}}$

Revision on differentation

Total questions: 23

Worksheet time: 15mins

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