Free Printable Differentiation

1.

What is the derivative of y = 2π?

a)

0

b)

2

c)

-2

d)

None of the above

2.

Differentiate y= 12x^-2

a)

24x^-1

b)

-24x^-3

c)

-24x^-1

d)

6x^-3

3.

Find the derivative of f(x) = 2x²+3.

a)

4x

b)

4x²

c)

3

d)

4x+3

4.

Differentiate 6x^⅔.

a)

4x^-⅓

b)

4x^-^⅔

c)

6x^⅓

d)

4x^⅓

5.

Choose the best rule to derive the function.

a)

Product rule

b)

Quotient rule

c)

Power rule

d)

Chain rule

6.

Find the derivative of

a)

sinx

b)

-sinx

c)

-cscx cotx

d)

sec²x

7.

Find the derivative of

a)

cscx cotx

b)

secx tanx

c)

sec²x

d)

-cscx cotx

8.

The derivative of sin(2x)

a)

2cos(x)

b)

2sin(2x)

c)

2cos(2x)

d)

2xcos(2x)

9.

The derivative of xcos(2x²)

a)

cos(2x²) - 4x²sin(2x²)

b)

sin(2x²) - 4x²cos(2x²)

c)

cos(2x²) + 4x²sin(2x²)

d)

cos(2x²) - 2x²cos(2x²)

10.

The derivative of cos(2x²)

a)

-2xcos(2x²)

b)

-4xcos(2x²)

c)

-sin(2x²)

d)

-4xsin(2x²)

11.

Find the derivative of f(x) = 2e^2x+ 3cosx.

a)

−3sin(x)

b)

4e2x + 3sin(x)

c)

4e2x

d)

4e2x − 3sin(x)

12.

Find the derivative of f(x) = 6x³⁰-2x¹⁵ + 4x³ - 2x + 1

a)

f'(x) = 18x²⁹+ 30x¹⁵ + 12x³

b)

f'(x) = 180x²⁹ - 30x¹⁴+ 12x²

c)

f'(x) = 180x²⁹ - 30x¹⁴+ 12x² - 2

d)

f'(x) = 180x²⁹ - 30x¹⁴+ 12x² +1

13.

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

14.

How much do you love mathematics ?

a)

suka sangat2

b)

mathematics? Yang ada nombor tu kan

c)

#siscuba

d)

biasa2 je

15.

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)

16.

$\frac{\text{d}}{\text{d}y}\left(e^x+2x\right)^3$

a)

$3\left(e^x+2\right)\left(e^x+2x\right)^2$

b)

$3\left(e^x+2\right)^2$

c)

$3\left(e^x+4x^2\right)\left(e^x+2x\right)^2$

d)

$4\left(e^x+2\right)^4$

17.

Differentiate y= 12x^-2

a)

24x^-1

b)

-24x^-3

c)

-24x^-1

d)

6x^-3

18.

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

a)

7

b)

0

c)

7x

d)

14

19.

Differentiate f(x) = 5x⁷.

a)

35x⁶

b)

210x⁵

c)

5x⁶

d)

1050x⁴

20.

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

a)

1/2x

b)

-2x

c)

2x

d)

-2x^-3

21.

Find $\frac{dy}{dx}$ for $y=\frac{3x+2^{ }}{2x+1}$ by using quotient rule.

a)

$-\frac{1}{\left(2x+1\right)^2}$

b)

$\frac{1}{\left(2x+1\right)^2}$

c)

$\left(2x+1\right)^{-2}$

d)

$2x+1$

22.

Find $\frac{dy}{dx}$ for $y=3x^2\left(5x+1\right)$ by using product rule.

a)

$45x^2-6x$

b)

$45x^2+6x^{-1}$

c)

$45x+6$

d)

$45x^2+6x$

23.

Use the product rule to find the derivative. $f\left(x\right)\ =\ -x^3\left(3x^4-2\right)$

a)

$-3x^2+12x^3$

b)

$-21x^3+6x$

c)

$-21x^6+6x^2$

d)

$-84x^6-6x^2$

24.

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

25.

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

a)

product rule

b)

quotient rule

c)

power rule

d)

sum rule

26.

Find the derivative

$y=\frac{3}{\sqrt[]{x+5}}$

a)

$\frac{\text{d}x}{\text{d}y}=\frac{3}{2}\left(x+5\right)^{\frac{3}{2}}$

b)

$\frac{\text{d}x}{\text{d}y}=\frac{-3}{2}\left(x+5\right)^{\frac{3}{2}}$

c)

$\frac{\text{d}x}{\text{d}y}=\frac{3}{2}\left(x+5\right)^{-\frac{3}{2}}$

d)

$\frac{\text{d}x}{\text{d}y}=-\frac{3}{2}\left(x+5\right)^{-\frac{3}{2}}$

27.

Find the derivative

$y=\sqrt[5]{x^3-4}$

a)

$\frac{\text{d}x}{\text{d}y}=\frac{1}{5}\left(x^3-4\right)^{\frac{4}{5}}$

b)

$\frac{\text{d}x}{\text{d}y}=\frac{3}{5}x^2\left(x^3-4\right)^{-\frac{4}{5}}$

c)

$\frac{\text{d}x}{\text{d}y}=\frac{3}{5}x^2\left(x^3-4\right)^{\frac{4}{5}}$

d)

$\frac{\text{d}x}{\text{d}y}=\frac{3}{5}\left(x^3-4\right)^{-\frac{4}{5}}$

28.

Differentiate f(x) = 4x².

a)

8x

b)

16x

c)

16x^2

d)

8x^2

29.

Differentiate f(x) = 5x⁷.

a)

35x^6

b)

210x^5

c)

5x^6

d)

1050x^4

30.

Differentiate y= 12x^-2

a)

24x^-1

b)

-24x^-3

c)

-24x^-1

d)

6x^-3

31.

Find the derivative of:
f(x) = -5/x⁴

a)

-20/x⁵

b)

20/x⁵

c)

-20/x³

d)

20/x³

32.

Find the derivative of:
f(x) = 5 - 2x

a)

5

b)

-2x

c)

-2

d)

2

33.

Find the derivative of:
f(x) = 2x²+ 3

a)

4x

b)

2x

c)

3

d)

2x+3

34.

Find the derivative of:
f(x) = 2x²- 7x + 9

a)

4x

b)

4x + 7

c)

4x - 7

d)

9

35.

Find the derivative of the given equation
f(x) = x³ + x² + 3

a)

3x² + 2x

b)

3x + 2x

c)

3x + 2x + 3

d)

x³ + x²

36.

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

a)

2x + 3

b)

2x - 4

c)

2x + 4

d)

2x - 3

37.

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

38.

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

39.

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

40.

Which rule would you need to use?

a)

Power Rule

b)

Product Rule

c)

Quotient Rule

d)

Chain Rule

41.

Find the derivative of this function

a)

(8x³ -60x/(2x²-5)²

b)

16x⁴/(2x²-5)²

c)

(8x⁴ -60x²)/(2x²-5)²

d)

3x/(2x²-5)²

Differentiation

Total questions: 41

Worksheet time: 52mins

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