product rule

Calculus Tutorial

product rule

Intro

Product rule (f(x)g(x))’=f(x)g'(x)+g(x)f'(x)
Differentiating Exponential function d/dx(ex)=ex

Sample Problem

y=x3.ex
find dy/dx

Solution

y=x3.ex
dy/dx=d/dx(x3.ex)
=x3.d/dx(ex)+ex.d/dx(x3) product rule
=x3.ex+ex.3×2 d/dx(ex)=ex
=x2.ex(x+3) simplify



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