# How do you implicitly differentiate #xy^2 + xy = 12#?

##### 1 Answer

Dec 24, 2015

#### Explanation:

Given

We can differentiate with respect to

This can be done by product rule like this

#=> y^2 + 2xy dy/dx + y + x(dy/dx) = 0 #

Keep all

#2xy (dy/dx) + x (dy/dx) = -y^2 -y#

Factor out

#dy/dx(2xy +x) = -y^2 -y#

Divide both side by

#(dy/dx)(2xy +x)/(2xy+x )=( -y^2 -y)/(2xy+x)#

#dy/dx = (-y^2 -y)/(2xy+x) = (-y(y+1))/(x(2y+1))#