## Calculus Tutorial

*Differentiating using multiple rule*

#### Intro

using the chain rule and product rule

#### Sample Problem

y=cos((x3+2).sin(x+1))

find dy/dx

#### Solution

y=cos((x3+2).sin(x+1))

dy/dx=d/dx(cos((x3+2).sin(x+1))) — differentiate

dy/dx=(-sin(x3+2).sin(x+1)).d/dx((x3+2).sin(x+1)) — chain rule

dy/dx=(-sin(x3+2).sin(x+1)).(d/dx(x3+2).sin(x+1)+d/dx(sin(x+1)).(x3+2)) — product rule

dy/dx=-sin(x3+2).sin(x+1).(3×2.sin(x+1)+cos(x+1).1.(x3+2))

dy/dx=-sin(x3+2)sin(x+1)(3×2.sin(x+1)+(x3+2)cos(x+1)) — simplify

# 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. |