Free Printable Grade 12 Derivatives

1.

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

a)

$f'(x)=7$

b)

$f'(x)=0$

c)

$f'(x)=7x$

d)

$f'(x)=14$

2.

Find the derivative of the given equation $f(x)=-4x$

a)

$f'(x)=-4$

b)

$f'(x)=x$

c)

$f'(x)=4$

d)

$f'(x)=0$

3.

Find the derivative of the given equation $f(x)=1-x^2$

a)

$f'(x)=1-2x$

b)

$f'(x)=-2x$

c)

$f'(x)=-2$

d)

$f'(x)=-1$

4.

Find $\frac{\text{d}y}{\text{d}x}$ if $y=\frac{2}{x}$

a)

$\frac{\text{d}y}{\text{d}x}=\frac{2}{x}$

b)

$\frac{\text{d}y}{\text{d}x}=\frac{-2}{x}$

c)

$\frac{\text{d}y}{\text{d}x}=\frac{-2}{x^2}$

d)

$\frac{\text{d}y}{\text{d}x}=\frac{2}{x^2}$

5.

Find the derivative of the given equation $f(x)=x^3+x^2+3$

a)

$f'(x)=3x^2+2x$

b)

$f'(x)=3x+2x$

c)

$f'(x)=3x+2x+3$

d)

$f'(x)=x^3+x^2$

6.

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

a)

$3x^3+2x$

b)

$3x^2+2$

c)

$3x+2$

d)

$3x$

7.

Find the derivative of the given equation $f(x)=\frac{1}{x^2}$

a)

$f'(x)=\frac{1}{2x}$

b)

$f'(x)=-2x$

c)

$f'(x)=2x$

d)

$f'(x)=\frac{-2}{x^3}$

8.

Find the derivative.
$f(z)=\frac{1}{3z^2}+4z^3$

a)

$f'(z)=6z^3+12z^2$

b)

$f'(z)=6z+12x^2$

c)

$f'(z)=-\frac{2}{3z^3}+12z^2$

d)

$f'(z)=-\frac{6}{z^2}+12z^2$

9.

Find the derivative.
$f(x)=\frac{4}{x}+x^4$

a)

$f'(x)=-4x^2+\frac{4}{x^3}$

b)

$f'(x)=-\frac{4}{x^2}-4x^3$

c)

$f'(x)=-\frac{4}{x^2}+4x^3$

d)

$f'(x)=4x^2-\frac{4}{x^3}$

10.

Find the derivative of $f(x)=-\frac{2}{3}x^3-\frac{1}{2}x^2+9x$

a)

$f'(x)=-2x^2-x+9$

b)

$f'(x)=-2x^2+x+9$

c)

$f'(x)=2x^2-x+9$

d)

$f'(x)=-2x^2-x-9$

11.

Find the second derivative of the function: $f(x)=2x-5x^6$

a)

$f''(x)=2-30x^5$

b)

$f''(x)=2x-30x^5$

c)

$f''(x)=-30x^5$

d)

$f''(x)=-150x^4$

12.

$Dx\left[\frac{3\sqrt{x}-4}{\sqrt{x}}\right]$

a)

$3-\frac{4}{\sqrt{x}}$

b)

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

c)

$\frac{4}{\sqrt{x^3}}$

d)

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

13.

Find the derivative of $y=2x^2(3x-4)$

a)

$\frac{\text{d}y}{\text{d}x}=6x^3-8x^2$

b)

$\frac{\text{d}y}{\text{d}x}=18x^2-16x$

c)

$\frac{\text{d}y}{\text{d}x}=15x^2-16x$

d)

$\frac{\text{d}y}{\text{d}x}=6x-8$

14.

Differentiate $f(x)=\frac{2}{x^5}-5$

a)

$f'(x)=x^5-3$

b)

$f(x)=-10x^6$

c)

$f(x)=x^5-5$

d)

$f(x)=-\frac{10}{x^6}$

15.

Find the derivative of $g(x)=(x+2)(2x+5)$

a)

$g'(x)=4x+9$

b)

$g'(x)=4x^2+9x$

c)

$g'(x)=9x^2+4$

d)

$g'(x)=2x^2+9x+10$

Grade 12 Derivatives

Total questions: 15

Worksheet time: 51mins

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