Question

Why does the chain rule work?

Answer 1

The chain rule is used to differentiate composite function, which are something of the form `f(g(x))`. The rule states that the derivative of such a function is the derivative of the outer function, evaluated in the inner function, times the derivative of the inner function. In formulas:

`d/dx (f(g(x)) = f'(g(x)) * g'(x)`.

You can iterate this procedure with multiple functions, so

`d/dx (f(g(h(x))) = f'(g(h(x))) * g'(h(x)) * h'(x)`, and so on