Free Printable MAT101_Tutorial01052025

1.

Find the derivative of

a)

cscx cotx

b)

secx tanx

c)

sec²x

d)

-cscx cotx

2.

The derivative of sin(2x)

a)

2cos(x)

b)

2sin(2x)

c)

2cos(2x)

d)

2xcos(2x)

3.

Differentiate 6x^⅔.

a)

4x^-⅓

b)

4x^-^⅔

c)

6x^⅓

d)

4x^⅓

4.

Find the derivative for $\sin\left(x^2\ +5\right)$

a)

$2x\cos\left(x^2\ +5\right)$

b)

$-x\cos\left(x^2\ +5\right)$

c)

$\cos\left(x^2+\ 5\right)$

d)

$-2x\cos\left(x^2+5\right)$

5.

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

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)

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

6.

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)

$2x+1$

7.

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

8.

Find the equation of tangent of the curve $y=\frac{12}{x^2-4x}$ at the point where $x=3$ .

a)

$y=-\frac{8}{3}x+4$

b)

$y=-\frac{8}{3}x-4$

c)

$3y=8x+4$

d)

$3y-8x+4=0$

9.

Which rule would you need to use?

a)

Power Rule

b)

Product Rule

c)

Quotient Rule

d)

Chain Rule

10.

Derivative means...

a)

slope of the tangent line

b)

slope of the normal line

c)

exponent

d)

potato

11.

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

a)

$12\tan^3x\sec^2x$

b)

$12\tan^3x\sec x$

c)

$12\sec^3x$

d)

$12\sec^6x$

e)

$12\sec^2x$

12.

Find the turning point of:

f(x) = 2x²- 8x + 9 (hint dy/dx=0)

a)

(2,1)

b)

(8,1)

c)

(2,10)

d)

(-2,1)

MAT101_Tutorial01052025

Total questions: 12

Worksheet time: 15mins

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