4.9 Differentiation of Implicit Functions
If an equation is expressed as y = f(x), then y is said to be the explicit function of x. However if y is connected with x by an expression f (x, y) = 0, then y is said to an implicit function of x. For e.g. x2 + 3xy + y2 = 0.
For differentiating the implicit function we differentiate each term w.r.to x keeping in mind that if there is a term contains powers of y, we differentiate first w.r.to. y and then multiply it by to get its differentiation w.r.to x.