ProLesson 3 of 36 min read

How the chain rule works

Learn to differentiate functions inside functions by multiplying the rates of change of each layer.

Many real formulas are layered: the area of a ripple depends on its radius, and the radius depends on time. In symbols, functions like (3x + 1)^2 or sqrt(x^2 + 1) have one function sitting inside another. The power rule from the first lesson cannot handle these directly. The chain rule can, and it is one of the most used rules in calculus.

Vidi Pro

Keep going with Pro.

The first lesson of every class is free. Pro opens every lesson in IELTS, Programming, Mathematics, Science and Data and AI, with practice questions.

Already have Pro? Log in to keep reading.

See Vidi Pro Log in

Written with AI help. Spotted a mistake? Tell us.