# How do you find #dy/dx# by implicit differentiation given #x/y+3y=2#?

##### 1 Answer

Feb 28, 2017

#### Explanation:

#x/y+3y=2#

#rArrx/y=2-3y# differentiate all terms on both sides

#color(blue)"implicitly with respect to x"#

#"differentiate "x/y" using the " color(blue)"quotient rule"#

#rArr(y.1-x.dy/dx)/(y^2)=0-3.dy/dx#

#rArry-xdy/dx=-3y^2dy/dx#

#rArrdy/dx(3y^2-x)=-y#

#rArrdy/dx=-y/(3y^2-x)#