Find derivative of f(x)=g(h(x))

Question

Would the derivative be something like:

g'(h(x))*h'(x) ??

Answer 1

yes. The good old chain rule. It helps to write them as fractions, so things cancel out:

dg/dx = dg/dh * dh/dx

I know they usually tell you to avoid thinking of derivatives as fractions, but they really are.

It's the same with parametric functions, x(t) and y(t)

dy/dx = (dy/dt) / (dx/dt)