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Differentiation Techniques

Secondary 3 Additional Math practice

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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=2x3+2xy = 2x^3 + \frac{2}{x} with respect to xx.
Show the worked solution
  • y=2x3+2x−1y = 2x^3 + 2x^{-1}
  • dydx=6x2−2x−2power rule\frac{dy}{dx} = 6x^2 - 2x^{-2} \quad \scriptsize\textit{power rule}
  • dydx=6x2−2x2\frac{dy}{dx} = 6x^2 - \frac{2}{x^2}

Answer: 6x2−2/x26x^2-2/x^2

Example 2

Differentiate y=(x2+5)4y = (x^2 + 5)^{4} with respect to xx.
Show the worked solution
  • y=(x2+5)4y = (x^2 + 5)^{4}
  • Let u=x2+5\text{Let } u = x^2 + 5
  • dydu=4u3,dudx=2x\frac{dy}{du} = 4u^{3}, \quad \frac{du}{dx} = 2x
  • dydx=4×2x×(x2+5)3chain rule\frac{dy}{dx} = 4 \times 2x \times (x^2 + 5)^{3} \quad \scriptsize\textit{chain rule}
  • dydx=8x(x2+5)3\frac{dy}{dx} = 8x(x^2 + 5)^{3}

Answer: 8x(x2+5)38x(x^2+5)^3

Example 3

Differentiate y=3x+3x+2y = \frac{3x + 3}{x + 2} with respect to xx.
Show the worked solution
  • y=3x+3x+2y = \frac{3x + 3}{x + 2}
  • Let f=3x+3,g=x+2\text{Let } f = 3x + 3, \quad g = x + 2
  • f′=3,g′=1f' = 3, \quad g' = 1
  • dydx=f′g−fg′g2quotient rule\frac{dy}{dx} = \frac{f'g - fg'}{g^2} \quad \scriptsize\textit{quotient rule}
  • =3(x+2)−(3x+3)(1)(x+2)2= \frac{3(x + 2) - (3x + 3)(1)}{(x + 2)^2}
  • dydx=3(x+2)2\frac{dy}{dx} = \frac{3}{(x + 2)^2}

Answer: 3/(x+2)23/(x+2)^2

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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