Differentiation Techniques practice questions

Secondary 3 topics from the Additional Mathematics 4049 syllabus. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

Practise differentiation techniques free

What this topic covers

Worked examples

Example 1

Differentiate y=4x3−1xy = 4x^3 - \frac{1}{x} with respect to xx.
Show the worked solution
  • $y = 4x^3 - x^{-1}$
  • $\frac{dy}{dx} = 12x^2 + x^{-2} \quad \scriptsize\textit{power rule}$
  • $\frac{dy}{dx} = 12x^2 + \frac{1}{x^2}$

Answer: 12x2+1/x212x^2+1/x^2

Example 2

Differentiate y=(3x2+3)4y = (3x^2 + 3)^{4} with respect to xx.
Show the worked solution
  • $y = (3x^2 + 3)^{4}$
  • $\text{Let } u = 3x^2 + 3$
  • $\frac{dy}{du} = 4u^{3}, \quad \frac{du}{dx} = 6x$
  • $\frac{dy}{dx} = 4 \times 6x \times (3x^2 + 3)^{3} \quad \scriptsize\textit{chain rule}$
  • $\frac{dy}{dx} = 24x(3x^2 + 3)^{3}$

Answer: 24x(3x2+3)324x(3x^2+3)^3

Example 3

Differentiate y=5x+22xy = \frac{5x + 2}{2x} with respect to xx.
Show the worked solution
  • $y = \frac{5x + 2}{2x}$
  • $\text{Let } f = 5x + 2, \quad g = 2x$
  • $f' = 5, \quad g' = 2$
  • $\frac{dy}{dx} = \frac{f'g - fg'}{g^2} \quad \scriptsize\textit{quotient rule}$
  • $= \frac{5(2x) - (5x + 2)(2)}{(2x)^2}$
  • $\frac{dy}{dx} = \frac{-4}{(2x)^2}$

Answer: −4/(2x)2-4/(2x)^2

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Which syllabus does this follow?

Additional Mathematics (4049), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.

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