Edexcel IGCSE·Further Pure Mathematics·IGCSE Further Pure Mathematics

Differentiation

13 min read

The power rule, tangents and normals, stationary points, and rates of change.

Differentiation finds the gradient of a curve at any point.

The power rule

$\text{if } y = x^n \text{ then } \frac{dy}{dx} = nx^{n-1}$ Rewrite roots/fractions as powers first.

Worked example. $y = 4x^3 - \dfrac{2}{x} = 4x^3 - 2x^{-1}$ , so $\dfrac{dy}{dx} = 12x^2 + 2x^{-2}$ .

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Edexcel IGCSE·Further Pure Mathematics·IGCSE Further Pure Mathematics

13 min read

The power rule, tangents and normals, stationary points, and rates of change.

Differentiation finds the gradient of a curve at any point.

$\text{if } y = x^n \text{ then } \frac{dy}{dx} = nx^{n-1}$ Rewrite roots/fractions as powers first.

Worked example. $y = 4x^3 - \dfrac{2}{x} = 4x^3 - 2x^{-1}$ , so $\dfrac{dy}{dx} = 12x^2 + 2x^{-2}$ .

Create a free account to read this note in full. Every free account gets 2 complete revision notes — no card needed.