## Calculus Tutorial

*Implicit differentiation*

#### Intro

In implicit differentiation, we differentiate both sides of the equation according to x and treat y as an implicit function of x

#### Sample Problem

3xy+x2-2y3=7

find dy/dx

#### Solution

3xy+x2-2y3=7

d/dx(3xy+x2-2y3)=d/dx(7) — differentiate

3.d/dx(xy)+d/dx(x2)-2.d/dx(y3)=d/dx(7)

3(y.1+x.dy/dx)+2x-2.3y2dy/dx=0 — produt rule and power rule

3y+3x.dy/dx+2x-6y2.dy/dx=0 — simplify

(3x+6y2)dy/dx=-3y-2x — simplify

dy/dx=-(2x+3y)/(3x+6y2)

# 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. |