Differentiation practice questions

To differentiate using the power rule, multiply by the power then reduce the power by one, so a x to the n becomes a n x to the n minus one. For y equals 4x cubed, the derivative is 12x squared. Substitute an x value into the derivative to find the gradient there.

Differentiation finds the rate of change of a function, and the gradient of a curve at any point. The power rule handles most A-level Pure questions: multiply by the power, then reduce the power by one.

The method, step by step

1. Apply the power rule. For axⁿ, the derivative is anxⁿ⁻¹.
2. Differentiate term by term. Each term is handled independently.
3. Constants vanish. The derivative of any number on its own is 0.
4. Substitute for a gradient. To find the gradient at a point, substitute the x value into the derivative.

Worked example

Common mistakes

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