A-Level · Maths
Chain rule
Also known as: differentiation of composite functions
What is chain rule?
The chain rule differentiates composite functions: if y = f(g(x)) then dy/dx = f'(g(x)) · g'(x). It appears across A-Level Maths and Further Maths whenever an outer function wraps an inner function — common examples are sin(2x), e^(3x²) and (1+x²)⁵. Without the chain rule, every composite differentiation drops marks; with it, the standard trick is to spot the inner function first.
Where it appears in exams
- Differentiate y = sin(3x²) — outer function sin, inner function 3x².
- Differentiate y = (1 + e^x)⁴ — outer power 4, inner 1+e^x.
- Implicit differentiation problems regularly need the chain rule inside an equation.
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