product rule

Calculus Tutorial

product rule

Intro

The product rule tells us how to find the derivative of the product of two functions.
d/dx(f(x)g(x))=f(x)d/dx(g(x))+g(x)d/dx(f(x))

Sample Problem

y=(x2+x+4)(2x+3)
find dy/dx.

Solution

y=(x2+x+4)(2x+3)
dy/dx=(x2+x+4).d/dx(2x+3)+(2x+3).d/dx(x2+x+4) product rule
dy/dx=(x2+x+4).2+(2x+3).(2x+1)
dy/dx=2×2+2x+8+4×2+2x+6x+3
dy/dx=6×2+10x+11 simplify



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