Implicit Differentiation Formula

Implicit differentiation is the procedure of differentiating an implicit equation with respect to the desired variable x while treating the other variables as unspecified functions of x.

To differentiate an implicit function, any of the following methods is followed :

  • In the first method, the implicit equation is solved for y and it is expressed explicitly in terms of x and differentiation of y is carried. This method is found useful only when y is easily expressible in terms of x.
  • In the second method, y is thought of as a function of x, and both members of the implicit equation are differentiated w.r.t x. The resulting equation is solved to find the value of $\frac{dy}{dx}$ .

Solved Examples

Question 1: Calculate the implicit derivative of $x^{2}-5xy+3y^{2}=7$ ?


Given implicit function is,






Practise This Question

is an example of which of the following types of reactions

[AFMC 1997; CPMT 1999]