Free Printable Higher Order Derivatives

1.

Find the derivative of

f\left(x\right)=\left(x^3+1\right)^7

a)

$7\left(3x^2+1\right)^6$

b)

$7\left(x^3+1\right)^6\left(3x^2\right)$

c)

$21x^2$

d)

$21x^2\left(x^{18}\right)$

2.

Find the derivative of

f\left(x\right)=\sqrt{x^2+8}

a)

$\left(x^2+8\right)^{\frac{1}{2}}$

b)

$\frac{1}{2}\left(x^2+8\right)^{\frac{3}{2}}\left(2x\right)$

c)

$x\left(x^2+8\right)^{\frac{1}{2}}$

d)

$\frac{1}{2}\left(x^2+8\right)^{-\frac{1}{2}}\left(2x\right)$

3.

Find the derivative of

f\left(x\right)=\frac{1}{x^4+3x}

a)

$-\left(x^4+3x\right)^{-2}\left(4x^3+3\right)$

b)

$\left(x^4+3x\right)^{-2}\left(4x^3+3\right)$

c)

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

d)

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

4.

Find the derivative of

f\left(x\right)=4x\left(3x-1\right)^2

a)

$24x\left(3x-1\right)^{-1}+\left(3x-1\right)^2$

b)

$24x\left(3x-1\right)+4\left(3x-1\right)^2$

c)

$24x\left(3x-1\right)^2+\left(3x-1\right)^2$

d)

$8x\left(3x-1\right)+12x$

5.

Find the second derivative of the following functions with respect to x.
y=3x⁴

a)

36x²

b)

12x³

c)

4x³

d)

12x²

6.

Find f "'(x) when

f(x)=10x⁵ +3x⁴ -5x³ +2x² -10x+6

a)

200x³+36x²-30x+4

b)

600x² +72x -26

c)

600x² +72x -30

d)

600x² +72x -36

7.

Find the second derivative of the function:
f (x) = 2x - 5x⁶

a)

f ''(x)= 2 - 30x

b)

f ''(x) = 2-30x⁵

c)

f ''(x) = -30x⁵

d)

f ''(x) = -150x⁴

8.

If the position of a particle is represented by x(t) = -t² + 1, what is its instantaneous velocity at t = 1?

a)

v = 0

b)

v = 1

c)

v = -1

d)

v = -2

9.

Find the second derivative of the following functions with respect to x.
y=(x³+x)/x²

a)

x+(1/x)

b)

1-(1/x²)

c)

2/x²

d)

2/x³

10.

FInd the derivative:
f(x) = (-2/3)x³ - (1/2)x² + 9x

a)

-2x² - x + 9

b)

-2x² + x + 9

c)

2x² - x + 9

d)

2x² - x - 9

11.

Find the second derivative of the function:
f (x) = 2x - 5x⁶

a)

f ''(x)= 2 - 30x

b)

f ''(x) = 2-30x⁵

c)

f ''(x) = -30x⁵

d)

f ''(x) = -150x⁴

12.

Find the second derivative of the following functions with respect to x.
y=3x²+5x-1

a)

6x+5

b)

3x+5

c)

5

d)

6

13.

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

14.

Find the derivative. f(x) = 1/(3x²) + 4x³

a)

f'(x) = 6x³ + 12x²

b)

f'(x) = 6x + 12x²

c)

f'(x) = -2/(3x³) + 12x²

d)

f'(x) = -6/x² + 12x²

15.

Find the derivative f(x) = (3x + 5)⁴

a)

f'(x) = 12(3x)³

b)

f'(x) = 12(3x + 5)³

c)

f'(x) = (3)⁴

d)

f'(x) = (3x + 5)³

16.

What rule should be used in deriving f(x) = x⁵

a)

Constant rule

b)

Sum rule

c)

Power rule

d)

Difference rule

17.

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

18.

What is the derivative of f(x) = 2x³- 4x + 5?

a)

f'(x) = 6x² - 4x

b)

f'(x) = 2/3x² - 4x

c)

f'(x) = 3x² - 4

d)

f'(x) = 6x² - 4

19.

Which function has the derivative of g'(x) = 4x³ + 2x - 1

a)

g(x) = 2x⁴ + 2x² - 1

b)

g(x) = x⁴ + x² - x

c)

g(x) = 2x³ + x³ - 2x

d)

g(x) = x⁵ + x² - x

20.

Choose the best rule to derive the function.

a)

Product rule

b)

Quotient rule

c)

Power rule

d)

Chain rule

21.

Let y = (x - 1)(x + 2). Find dy/dx.

a)

2x + 1

b)

2x - 1

c)

4x - 1

d)

2x² + x - 1

Higher Order Derivatives

Total questions: 21

Worksheet time: 4hrs 30mins

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