Chain Rule

The Chain Rule is a method in calculus for finding the derivative of a composed function—meaning a function inside another function. Imagine two functions, say \(f\) and \(g\), where the output of \(g\) becomes the input of \(f\). The Chain Rule tells us that to find how the overall function changes, we multiply the rate at which \(f\) changes with respect to \(g\) by the rate at which \(g\) changes with respect to its input. This approach allows us to differentiate complex, layered functions by breaking them down into simpler parts.