Find derivative after algebraic simplification (fractional/mixed powers)

Differentiate expressions that first require algebraic manipulation (e.g. expanding brackets, splitting fractions, or rewriting roots) to obtain terms with fractional or mixed powers before differentiating.

28 questions · Easy -1.2

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Edexcel C1 Q2
4 marks Easy -1.8
Differentiate with respect to \(x\) $$3x^2 - \sqrt{x} + \frac{1}{2x}.$$ [4]
Edexcel C2 Q5
10 marks Moderate -0.8
  1. Differentiate \(2x^2 + \sqrt{x} + \frac{x^2 + 2x}{x^2}\) with respect to \(x\) [5]
  2. Evaluate \(\int_1^4 \left(\frac{x}{2} + \frac{1}{x^2}\right) dx\). [5]
OCR MEI C2 2016 June Q1
5 marks Easy -1.3
  1. Find \(\frac{\mathrm{d}y}{\mathrm{d}x}\) when \(y = 6\sqrt{x}\). [2]
  2. Find \(\int \frac{12}{x^2} \mathrm{d}x\). [3]