Learning objectives
Explain the derivative as the limit of the gradients of chords through a point, and use the notations dy/dx, f′(x), d²y/dx² and f″(x)
Differentiate kxⁿ for any rational n, together with sums and differences, after rewriting roots and reciprocals such as 4/√x as powers of x
Use the chain rule to differentiate composite functions such as (3x − 5)⁴ and √(2x² + 1)
Find the gradient at a point on a curve and the equations of the tangent and the normal at that point
Use the sign of dy/dx to determine where a function is increasing or decreasing, including showing that a function is increasing for all x
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