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Differentiation

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

(fgh)'=f'gh+fg'h+fgh'
 
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