Understanding the Chain Rule in Calculus

The chain rule is a fundamental concept in calculus, specifically in the context of derivatives. It is used to find the derivative of composite functions. In simple terms, it allows us to differentiate a function within a function. Mathematically, if we have a function

[ f(x) = g(h(x)) ]

then the chain rule states that the derivative of ( f(x) ) with respect to ( x ) is given by

[ f'(x) = g'(h(x)) \cdot h'(x) ]

This rule is crucial in solving complex derivatives, and forms the basis for understanding the behavior of functions in calculus.