Differentiate the outer function, keeping the inner function the same.How to Do the Chain Rule To do the chain rule: Such functions must be differentiable themselves.The function must be a composite function of two or more functions.To use the chain rule, the following rules are required: In words, the chain rule requires finding the derivative of the outer function while keeping the inner function the same and then multiplying this by the derivative of the inner function. g(𝑥) is the inner function and f(𝑥) is the outer function. The chain rule is defined as, where u is a function of 𝑥 ( u = g(x) ) and y is a function of u ( y = f(u) ).Īlternatively, the chain rule can be written in function notation as F'(𝑥) = f'(g(𝑥)).g'(𝑥), where F(𝑥) = f(g(𝑥)). The chain rule is used when a function is within another function.
