Free Printable Differentiation

1.

How are you today?

4 lines

2.

Have you bought takeaways this week? If so, what was your favourite?

4 lines

3.

Find the derivative of f(x) = 2x⁵+3x

a)

10x⁴+3

b)

2x⁴+3

c)

10x⁵+3

d)

10x⁵+3x

4.

What is the derivative of xⁿ?

a)

(n-1)xⁿ

b)

nxⁿ⁺¹

c)

(n+1)x^n-1

d)

nx^n-1

5.

Find the second derivative of:

f(x) = 2x²- 8x + 9

a)

-8

b)

4

c)

9

d)

0

6.

Find the turning points of

y = x³+3x²-9x+1

(hint dy/dx=0)

a)

(-3,28) and (1,-4)

b)

(3,28) and (1,4)

c)

(1,28) and (-3,-4)

d)

(3,28) and (-1,-4)

7.

What is the derivative of f?

a)

1/(x - 1)^-1

b)

-1/(x - 1)^-2

c)

-1/(x - 1)

d)

-1/(x - 1)²

8.

Differentiate $\ y=e^{\left(7-9x\right)}$

a)

$-9e^{\left(7-9x\right)}$

b)

$e^{-9}$

c)

$-9\ln\left(7-9x\right)$

d)

$7e^{\left(7-9x\right)}$

9.

Given the function $f\left(x\right)=x^3+x^2-8x-2$ . Find the intervals on which f(x) is increasing.

a)

(a) $-\frac{4}{3}<x<2$

b)

(a) $x<-\frac{4}{3},\ x>2$

c)

(a) $-2<x<\frac{4}{3}$

d)

(a) $x<-2,\ x>\frac{4}{3}$

10.

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

11.

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

12.

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

a)

product rule

b)

quotient rule

c)

chain rule

d)

trapezium rule

13.

Find the derivative:
y=5x²e^3x

a)

y'=10xe^3x(2x+3)

b)

y'=5xe^3x(3x+2)

c)

y'=10ex^3x(3x+2)

d)

y'=5xe^3x(2x+3)

14.

hint: use quotient rule

a)

8x⁴ -60x²

b)

16x⁴

c)

(8x⁴ -60x²)/(2x²-5)²

d)

3x

15.

Find dy/dx

x=5t\ ^2+3,\ \ \ \ \ y=10t+4

a)

$\frac{\text{1}}{\text{t}}$

b)

$\frac{7}{t}$

c)

100t

d)

20t

16.

Find dy/dx

x=\sin\theta\ ,\ \ \ y=\cos\theta

a)

$\frac{-\sin\theta}{\cos\theta}=\ -\tan\ \theta$

b)

$\frac{\cos\theta}{\sin\theta}=\cot\ \theta$

c)

$\frac{\sin\theta}{\sin\theta}=1$

d)

$\frac{-\sin\theta}{\sin\theta}=-1$

17.

The parametric equations of a curve are x = t - e^tand y = t + e^-t. Find the coordinates of the stationary point.

a)

(1,0)

b)

(0,-1)

c)

(1,1)

d)

(-1,1)

18.

Find the x value(s) where f'(x) = 0

write values only

(a)

19.

Find the x value(s) where f(x) is not continuous.

Write values only separated by a comma.

(a)

20.

Find the x-values where f(x) is not differentiable.

write values only separated by a comma and no spaces

(a)

21.

Evaluate f(1) or write DNE if it does not exist.

(a)

22.

Evaluate $\lim_{x\rightarrow1}\ f\left(x\right)$ or write DNE if it does not exist.

(a)

23.

Evaluate $\lim_{x\rightarrow0}\ f\left(x\right)$ or write DNE if it does not exist.

(a)

24.

write answer to 2dp

(a)

Differentiation

Total questions: 24

Worksheet time: 32mins

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