On occasions that a function F(x , y) = 0 can not be defined in the explicit form
= f(x) then the implicit form F ( x , y) = 0 can be used as basis in defining the
derivative of y ( the dependent variable) with respect to x ( the independent
When differentiating F( x, y) = 0, consider that y is defined implicitly in terms of
x , then apply the chain rule. As a rule,
Differentiate both sides of the equation with respect to x.
Collect all terms involving dy/dx on the left side of the equation and the rest
of the terms on the other side.
Factor dy/dx out of the left member of the equation and solve for dy/dx by
dividing the equation by the coefficient of dy/dx.