## 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

# About The Author

Mathematics Teacher |

I was a teacher in Srilanka from 1992 to 2006. I took tuition from 1990 to 1991 in India. I do general work in Canada but I help to do homework to my daughters. I finished my teacher\'s training college diploma in Srilanka. I completed my B.Sc degree course at Bharayiar university in India. |