Differentiation

Question

Derive the product rule for the differentiation of the product of three differentiable functions, that is , d/dx(f(x)g(x)h(x)).

 

 

Thank You!

Answer 1

(fgh)'=f'gh+fg'h+fgh'

 

Answer 2

d/dx(f(x)g(x)h(x))=f(x)d/dx(g(x)h(x))+g(x)h(x)df/dx=f(gdh/dx +hdg/x)+ghdf/dx=fgdh/dx+fhdg/dx+ghdf/dx

 

The idea is to apply the product rule twice…the notation gets a little messy with a keyboard

 

Jim