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Differentiating powers of xEdexcel International A Level Maths: Mind map

The rule
Term by term

Differentiating powers

$x^n\to nx^{n-1}$

multiplyreduce powerterm by term
Rewrite first
Brackets and fractions
Use the gradient

Exam questions on Differentiating powers of x

  1. A curve has equation y=3x4−2x2+7x−5y=3x^4-2x^2+7x-5.
    Find the gradient of the curve at the point where it crosses the yy-axis.2 marks
  2. A curve has equation y=f(x)y=f(x), where f(x)=(2x+5)(x−1)f(x)=(2x+5)(x-1).
    The curve crosses the positive xx-axis at the point AA. Find the gradient of the curve at AA.2 marks
  3. A curve has equation y=x2+5x−33xy=\dfrac{x^2+5x-3}{3x} for x≠0x\neq0.
    Find dydx\frac{\mathrm{d}y}{\mathrm{d}x}.3 marks
See the full worksheet

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).