MathematicsCode 9709
Differentiation
What this topic asks you to be able to do
- understand the gradient at a point on a curve as the limit approached by chord gradients over a suitable sequence of chords, and write first derivatives as f ′(x) or dy/dx and second derivatives as f ″(x) or d²y/dx²
- apply the derivative of x^n, where n is any rational number, along with constant multiples, sums and differences of functions, and use the chain rule for composite functions
- use differentiation in working with gradients, tangents and normals, functions that are increasing or decreasing, and rates of change
- find the stationary points of a curve, decide what type each one is, and use what you know about them when sketching graphs