Derivative of Implicit Functions

Since the functions can not be expressed in terms of one specific variable, we have to follow a different method to find the derivative of the implicit function :

While computing the derivative of the Implicit function, our aim is to solve for dy/dx or any higher-order derivatives depending on the function. To solve dy/dx in terms of x and y, we have to follow certain steps:

Implicit functions are functions where a specific variable cannot be expressed as a function of the other variable. A function that depends on more than one variable.  Implicit Differentiation helps us compute the derivative of y with respect to x  without solving the given equation for y, this can be achieved by using the chain rule which helps us express y as a function of x. 

 Implicit Differentiation can also be used to calculate the slope of a curve, as we cannot follow the direct procedure of differentiating the function y = f(x) and putting the value of the x-coordinate of the point in dy/dx to get the slope. Instead, we will have to follow the process of implicit differentiation and solve for dy/dx.

The method of implicit differentiation used here is a general technique to find the derivatives of unknown quantities.

Example

x²y² + xy²+ e^xy = abc = constant

The function above is an implicit function, we cannot express x in terms of y or y in terms of x.