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Year 12 · Calculus

Differentiate with the power rule

The derivative measures how fast a function changes: the gradient at any point.

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How to do it

  1. Power rule: bring the power down in front, then reduce it by 1.
  2. The derivative of a constant is 0.
  3. For the gradient at a point, substitute x into the derivative.

Worked example

Find f'(x) if f(x) = 2x⁴ − x − 2
Power rule: bring the power down and reduce it by one. d/dx(2x^4) = 8x^3, d/dx(-1x) = -1, and a constant differentiates to 0. So f'(x) = 8x^3 − 1.
Answer: 8x^3-1

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Reduce the power by exactly 1.

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