Derivatives of Implicit Functions

In equations where y as a function of x cannot be explicitly defined by the variables x and y, we use implicit differentiation. If f(x,y) =0 , then differentiate with respect to x and group the terms containing dy/dx at one side and then solve for dy/dx.

For example, 2x + y = 12

d/dx(2x + y)= 0

2 + dy/dx = 0

dy/dx = -2