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LearnEdexcelYMA012018 specificationWMA11 · Pure Mathematics 1Differentiation

WMA11 · Module

Differentiation

4 subtopics≈ 140 min in total

Start the module: Gradients and the power rule Open graphing calculator

Gradients and the power rule
What the gradient of a curve means, how chords close in on the tangent, and the power rule $\dfrac{d}{dx}x^n=nx^{n-1}$ that makes differentiating fast, including roots, fractions and second derivatives.
≈ 45 min
Differentiating powers of x
The derivative $\dfrac{dy}{dx}$ is the gradient of a curve, found as the limit of the gradients of shorter and shorter chords. For powers of $x$ there is a one-line rule: bring the power down and reduce it by one. Rewrite roots and fractions as powers first.
≈ 30 min
Gradients, rates of change and second derivatives
Substitute an $x$ -value into $\dfrac{dy}{dx}$ to get the gradient there; set $\dfrac{dy}{dx}$ equal to a number to find where the curve has that gradient. Differentiating again gives the second derivative $\dfrac{d^2y}{dx^2}$ , the rate at which the gradient itself changes.
≈ 30 min
Tangents and normals
The tangent at a point has the curve's gradient there; the normal is perpendicular to it, with gradient $-\dfrac1m$ . Either way you need a point and a gradient, then $y-y_1=m(x-x_1)$ .
≈ 35 min