A-level · Differentiation

Differentiating powers of xExam-style questions

Finding how steep a curve is at any point. What a derivative measures and where it comes from; the power rule and why the power comes down; numbers in front, sums and constants; rewriting roots and fractions as powers; negative and fractional powers; using the gradient function at a point and backwards; and differentiating twice.

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16 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
Differentiate the following with respect to $x$ .
(a) $\dfrac{6}{x^3} + 4\sqrt{x}$

(2 marks)
(b) $x^2e^{3x}$

(2 marks)
(c) $\dfrac{2x + 1}{x - 3}$

(3 marks)
Level 2 · 7 marksTry it
2
Differentiate $y = \dfrac{(2x - 3)^2}{\sqrt{x}}$ by writing it as a sum of powers of $x$ .
Level 3 · 4 marksTry it
3
Find the coordinates of the stationary points of the curve $y = x + \dfrac{4}{x}$ .
Level 3 · 4 marksTry it
4
The curve $C$ has equation $y = 2\sqrt{x} - x$ . Find an equation of the tangent to $C$ at the point where $x = 4$ .
Level 3 · 4 marksTry it
5
The curve $C$ has equation $y = \dfrac{(x^2 - 1)^2}{x}$ , $x \ne 0$ . Find the coordinates of the stationary points of $C$ .
Level 3 · 5 marksTry it

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