Quotient rule

Calculus Tutorial

Quotient rule

Intro

The quotient tells us how to find derivative of the quotient of two functions.
d/dx(f(x)/g(x))=d/dx(f(x)).g(x)-f(x).d/dx(g(x))/(g(x))2

Sample Problem

y=cos(x)/x3
find dy/dx

Solution

y=cos(x)/x3
dy/dx=d/dx(cos(x)/x3)
=(d/dx(cos(x)).x3-cos(x).d/dx(x3))/(x3)2 quotient rule
=(-sin(x).x3-cos(x).3×2)/x6 differentiate cos(x) and x3
=-x2(xsin(x)+3cos(x))/x6 simplify
=-(xsin(x)+3cos(x))/x4 cancel common factors



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