Free Printable 9.2 Differentiation of a function

1.

Find the derivative of $y=\left(2-3x\right)^{88}$

a)

$\frac{dy}{dx}=88\left(2-3x\right)^{87}\left(-3\right)$

b)

$\frac{dy}{dx}=88\left(2-8x\right)^{87}\left(-8\right)$

c)

$\frac{dy}{dx}=88\left(2-3x\right)^{88}\left(-3\right)$

d)

$\frac{dy}{dx}=87\left(2-3x\right)^{87}\left(-3\right)$

2.

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

3.

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

4.

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

5.

Differentiate 6x^⅔.

a)

4x^-⅓

b)

4x^-^⅔

c)

6x^⅓

d)

4x^⅓

6.

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

7.

What is the derivative of y = 2π?

a)

0

b)

2

c)

-2

d)

None of the above

8.

Find $\frac{dy}{dx}$ for $y=x^5-\frac{3}{x^3}$ .

a)

$5x^3+\frac{9}{x^4}$

b)

$5x^3+9x^{-4}$

c)

$5x^4+\frac{9}{x^4}$

d)

$5x^4+\frac{9}{x^{-4}}$

9.

Find $\frac{dy}{dx}$ for $y=\left(x+5\right)\left(2x-1\right)$ .

a)

$9-4x$

b)

$4x+9$

c)

$4x-9$

d)

$-4x-9$

10.

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)

$45x^2+6x$

11.

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)

$2x+1$

12.

Find $\frac{d^2y}{dx^2}$ for $y=x^3\left(x^2+5\right)$ .

a)

$5x^4+15x^2$

b)

$5x^4-15x^2$

c)

$20x^3+30x$

d)

$20x^3-30x$

13.

$y=\frac{1}{2x^2}+\sqrt{x}$

a)

$\frac{1}{2\sqrt{x}}-\frac{1}{x^3}$

b)

$-\frac{1}{2\sqrt{x}}-\frac{1}{x^3}$

c)

$\frac{1}{2\sqrt{x}}-\frac{1}{x^2}$

d)

$-\frac{1}{2\sqrt{x}}-\frac{1}{x^2}$

14.

Differentiate the function below with respect to x

8x^2-\frac{4}{x}

a)

$16x+\frac{4}{x^2}$

b)

$8x+\frac{4}{x^2}$

c)

$16x-\frac{4}{x^2}$

d)

$16x-4x$

15.

Find $\frac{dy}{dx}$ for $y=\frac{3x+2^{ }}{2x+1}$

a)

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

b)

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

c)

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

d)

$2x+1$

16.

Find the derivative for

f\left(x\right)=\left(25-x^2\right)^{\frac{1}{2}}

a)

$-x\left(25-x^2\right)^{\frac{1}{2}}$

b)

$-2\left(25-x^2\right)^{\frac{1}{2}}$

c)

$-x\left(25-x^2\right)^{-\frac{1}{2}}$

d)

$-2x\left(25-x^2\right)^{-\frac{1}{2}}$

17.

Solve $\lim_{h\rightarrow0}\ \frac{\left(x+h\right)^3-x^3}{h}$

a)

$3x^2$

b)

$x^3$

c)

$6x$

d)

$3x^2+x^3$

18.

What is the derivative of

\sqrt{x^3}

a)

$\frac{3\sqrt{x}}{2}$

b)

$\frac{1}{2\sqrt{x}}$

c)

$\frac{3}{2\sqrt{x}}$

d)

$\frac{\sqrt{x}}{2}$

19.

What is the derivative of $\frac{1}{\sqrt{x}}$

a)

$\frac{\sqrt{x^3}}{2}$

b)

$\frac{-\sqrt{x^3}}{2}$

c)

$\frac{-\sqrt{x}}{2}$

d)

$\frac{\sqrt{x}}{2}$

20.

Find the x-coordinates of the points on the graph of $f\left(x\right)=\frac{2}{3}x^3-\frac{9}{2}x^2-3x+8$ when the gradient is 2

a)

$x=0.5\ and\ 5$

b)

$x=-0.5\ and\ 5$

c)

$x=0.5\ and\ \ -5$

d)

$x=-0.5\ and\ -5$

9.2 Differentiation of a function

Total questions: 20

Worksheet time: 19mins

Similar Resources on Wayground