Derivatives of Implicit Functions


Until now we have been differentiating various functions given in the form y = f(x). But it is not necessary that functions are always expressed in this form. For example, consider one of the following relationships between x and y:
x – y – π = 0 
x + sin xy – y = 0 
In the first case, we can solve for y and rewrite the relationship as y = x – π. In the second case, it does not seem that there is an easy way to solve for y. Nevertheless, there is no doubt about the dependence of y on x in either of the cases. When a relationship between x and y is expressed in a way that it is easy to solve for y and write y = f(x), we say that y is given as an explicit function of x. In the latter case it  is implicit that y is a function of x and we say that the relationship of the second type, above, gives function implicitly. In this subsection, we learn to differentiate implicit functions.

If you would like to contribute notes or other learning material, please submit them using the button below. | Implicit Differentiation

Next video

Implicit Differentiation [00:07:07]
Series: 1


View all notifications
Create free account

      Forgot password?
View in app×