Differentiation of Trig, Exp and Log practice questions

Secondary 4 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 of trig, exp and log free

What this topic covers

Worked examples

Example 1

Differentiate y=4sin⁡(2x)+2cos⁡(x)+4xy = 4\sin(2x) + 2\cos(x) + 4x with respect to xx.
Show the worked solution
  • $y = 4\sin(2x) + 2\cos(x) + 4x$
  • $\frac{dy}{dx} = 8\cos(2x) - 2\sin(x) + 4 \quad \scriptsize\textit{differentiate each term}$

Answer: 8cos(2x)−2sin(x)+48cos(2x)-2sin(x)+4

Example 2

Differentiate y=4e2x+2x2−3xy = 4e^{2x} + 2x^2 - 3x with respect to xx.
Show the worked solution
  • $y = 4e^{2x} + 2x^2 - 3x$
  • $\frac{dy}{dx} = 8e^{2x} + 4x - 3 \quad \scriptsize\textit{differentiate each term}$

Answer: 8e2x+4x−38e^{2x}+4x-3

Example 3

Differentiate y=5ln⁡(4x+3)y = 5\ln(4x + 3) with respect to xx.
Show the worked solution
  • $y = 5\ln(4x + 3)$
  • $\frac{dy}{dx} = 5 \cdot \frac{4}{4x + 3} \quad \scriptsize\textit{chain rule}$
  • $\frac{dy}{dx} = \frac{20}{4x + 3}$

Answer: 20/(4x+3)20/(4x+3)

Questions parents ask

Is it really free?

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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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