# The derivative of f(x)*g(x)/h(x)

What is the derivative rule for a function times another function divided by another function?

Pengwuino
Gold Member
Just treat f(x)*g(x) as one function, say v(x). So you have the derivative of $${{v(x)} \over {h(x)}}$$ which you differentiate like normal. When you differentiate v(x), you'll simply have a product rule to deal with.

mathman
It is easiest to do in two steps:
[(fg)'h - fgh']/h2 = [f'gh + fg'h - fgh']/h2

Thank you, I was trying to verify if that worked by doing it both ways. I figured out my problem. I had the signs on the v(x)/h(x) derivative rule switched.