Free Printable Aku & Maths: Takkan Terpisah (LEVEL 3)

1.

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

a)

5

b)

-2x

c)

-2

d)

2

2.

Find the derivative of:
f(x) = 2x²+ 3

a)

4x

b)

2x

c)

3

d)

2x+3

3.

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

4.

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

a)

2x + 3

b)

2x - 4

c)

2x + 4

d)

2x - 3

5.

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

6.

Find the derivative:
y= $\frac{2}{\sqrt[]{3x}}$

a)

y'= $\frac{1}{\sqrt[]{3x^3}}$

b)

y'= $\frac{-1}{\sqrt[]{\left(3x\right)^3}}$

c)

y'= $\frac{1}{\sqrt[]{\left(3x\right)^3}}$

d)

y'= $\frac{-1}{\sqrt[]{3x^3}}$

7.

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

a)

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

b)

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

c)

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

d)

$3x^2-2x\left(2xe^x+\frac{1}{e^x}\right)$

8.

Given $f(x)=x^2-\frac{6}{x}$ , find the value of x for which the second derivative $f''(x)=0$ .

a)

$\sqrt[3]{-6}$

b)

$\sqrt[3]{6}$

c)

$\sqrt[3]{-3}$

d)

$\sqrt[3]{3}$

9.

Given $y=\sqrt[]{x}\left(\frac{3}{x}-5\right)$ , find $\frac{dy}{dx}$

a)

$-\frac{3}{2\sqrt[]{x^3}}-\frac{5}{2\sqrt[]{x}}$

b)

$-\frac{3}{2\sqrt[]{x^3}}+\frac{5}{2\sqrt[]{x}}$

c)

$\frac{3}{2\sqrt[]{x^3}}-\frac{5}{2\sqrt[]{x}}$

d)

$\frac{3}{2\sqrt[]{x^3}}+\frac{5}{2\sqrt[]{x}}$

10.

FInd the derivative of $f\left(x\right)=\frac{6x^2+4x-3}{2x}$ .

a)

$f'\left(x\right)=3+\frac{3}{2x^2}$

b)

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

c)

$f'\left(x\right)=\frac{12x+4}{2}$

d)

$f'\left(x\right)=3+\frac{2}{3x^2}$

11.

Differentiate $f\left(x\right)=\frac{x+3}{1-x}$ ?

a)

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

b)

$f'\left(x\right)=\frac{-4}{\left(1-x\right)^2}$

c)

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

d)

$f'\left(x\right)=\frac{4}{\left(1-x\right)^2}$

e)

$f'\left(x\right)=\frac{3}{\left(1-x\right)^2}$

12.

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)

$45x^2+6x$

13.

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)

$2x+1$

14.

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)

$20x^3-30x$

15.

Find $\frac{dy}{dx}$ for $\sqrt[]{3x}$

a)

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

b)

$\frac{-\ \sqrt[\ ]{3}}{2\ \ \sqrt[]{x}}$

c)

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

d)

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

Aku & Maths: Takkan Terpisah (LEVEL 3)

Total questions: 15

Worksheet time: 36mins

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