Mathematics (AS)·Differentiation · NSSCAS 1.8.2
The chain rule
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Some functions live inside other functions — like (2x + 3)⁵. Expanding that bracket would take a whole page, but the chain rule differentiates it in one line. In this lesson Miss Eve teaches you both the careful u-substitution layout and the quick bracket method, works five full examples including roots and fractions, and shows you the trap that costs the most marks at AS. By the end you will find gradients of composite functions confidently, ready for tangents and normals.
What you'll learn in this lesson
By the end you should be able to (NSSCAS Mathematics (AS) 1.8.2):
- Differentiate composite functions built from powers of x using the chain rule, including roots and negative powers, and evaluate the gradient at a given point
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Miss Eve and Mike talk through the whole topic — with the figure and working drawn live.