# How does implicit differentiation work?

##### 1 Answer

Aug 5, 2014

Implicit differentiation is a way of differentiating when you have a function in terms of both x and y. For example:

#x^2+y^2=16#

This is the formula for a circle with a centre at (0,0) and a radius of 4

So using normal differentiation rules

#d/dx(x^2)+d/dx(y^2)=d/dx(16)#

#2x+d/dx(y^2)=0#

To find

#d/dx=d/dy *dy/dx#

#d/dy(y^2)=2y*dy/dx#

#2x+2y*dy/dx=0#

Rearrange for

#dy/dx=(-2x)/(2y#

#dy/dx=-x/y#

So essentially to use implicit differentiation you treat y the same as an x and when you differentiate it you multiply be

Youtube Implicit Differentiation

Theres another video on the subject here