## Calculus Tutorial

*product rule*

#### Intro

product rule :(f(x)g(x))’=f(x)g'(x)+g(x)f'(x)

differentiating trigonometric functions: d/dx(sin(x))=cos(x), d/dx(cos(x)=-sin(x)

differentiating logarithmic function: d/dx(ln(x))=1/x

#### Sample Problem

#### Solution

f(x)=ln(x)sin(x)

f'(x)=d/dx(ln(x)sin(x))

=ln(x).d/dx(sin(x))+sin(x).d/dx(ln(x)) product rule

=ln(x).cos(x)+sin(x).1/x differentiate ln(x) and sin(x)

=ln(x)cos(x)+sin(x)/x

# 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. |