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Differentiation of Trigonometric, Exponential and Logarithmic Functions

Secondary 4 Additional Math practice

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Differentiation of Trigonometric, Exponential and Logarithmic Functions 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 Trigonometric, Exponential and Logarithmic Functions free

What this topic covers

Worked examples

Example 1

Differentiate y=2sin⁡(2x)+3cos⁡(x)−3xy = 2\sin(2x) + 3\cos(x) - 3x with respect to xx.
Show the worked solution
  • y=2sin⁡(2x)+3cos⁡(x)−3xy = 2\sin(2x) + 3\cos(x) - 3x
  • dydx=4cos⁡(2x)−3sin⁡(x)−3differentiate each term\frac{dy}{dx} = 4\cos(2x) - 3\sin(x) - 3 \quad \scriptsize\textit{differentiate each term}

Answer: 4cos(2x)−3sin(x)−34cos(2x)-3sin(x)-3

Example 2

Differentiate y=e3x+2x2+2xy = e^{3x} + 2x^2 + 2x with respect to xx.
Show the worked solution
  • y=e3x+2x2+2xy = e^{3x} + 2x^2 + 2x
  • dydx=3e3x+4x+2differentiate each term\frac{dy}{dx} = 3e^{3x} + 4x + 2 \quad \scriptsize\textit{differentiate each term}

Answer: 3e3x+4x+23e^{3x}+4x+2

Example 3

Differentiate y=3ln⁡(x+5)y = 3\ln(x + 5) with respect to xx.
Show the worked solution
  • y=3ln⁡(x+5)y = 3\ln(x + 5)
  • dydx=3⋅1x+5chain rule\frac{dy}{dx} = 3 \cdot \frac{1}{x + 5} \quad \scriptsize\textit{chain rule}
  • dydx=3x+5\frac{dy}{dx} = \frac{3}{x + 5}

Answer: 3/(x+5)3/(x+5)

Questions parents ask

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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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