Differentiation

Introduction to Differentiation: Gradients, Notation and the Power RuleSign up

understand the derivative of f(x) as the gradient of the tangent to the graph of y = f(x) at a general point, and use the notations dy/dx and f'(x) · be able to differentiate x^n for any rational n, including sums and constant multiples of such terms · be able to differentiate from first principles for simple polynomial functions

Tangents, Normals and Increasing/Decreasing FunctionsSign up

be able to find equations of tangents and normals to a curve at a given point · be able to locate stationary points of a curve and determine their nature using the second derivative or sign of the first derivative · be able to apply differentiation to problems involving rates of change, optimisation and curve sketching

Stationary Points, Their Nature and Curve SketchingSign up

be able to find and classify stationary points (maxima, minima, points of inflection) using the second derivative test · be able to apply differentiation to optimisation problems involving maxima and minima in geometric and applied contexts

Connected Rates of ChangeSign up

be able to use the chain rule to solve related-rates problems where one variable is changing as a known function of time and another depends on it