Basic power rule differentiation

Questions asking to differentiate simple polynomials and power functions (including negative and fractional powers) without composition, using only the power rule.

28 questions · Easy -1.1

1.07i Differentiate x^n: for rational n and sums

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AQA AS Paper 1 2021 June Q2

1 marks Easy -1.8

Given that \(\frac{dy}{dx} = \frac{1}{x}\) find \(\frac{d^2y}{dx^2}\) Circle your answer. [1 mark] \(-\frac{2}{x^2}\) \(-\frac{1}{x^2}\) \(\frac{1}{x^2}\) \(\frac{2}{x^2}\)

AQA AS Paper 2 2020 June Q3

3 marks Moderate -0.8

It is given that $$y = 3x^4 + \frac{2}{x} - \frac{x}{4} + 1$$ Find an expression for \(\frac{d^2y}{dx^2}\) [3 marks]

AQA Paper 1 Specimen Q2

1 marks Easy -1.8

A curve has equation \(y = \frac{2}{\sqrt{x}}\) Find \(\frac{dy}{dx}\) Circle your answer. [1 mark] \(\frac{\sqrt{x}}{3}\) \quad \(\frac{1}{x\sqrt{x}}\) \quad \(-\frac{1}{x\sqrt{x}}\) \quad \(-\frac{1}{2x\sqrt{x}}\)