Derivative of an Implicit Function

To differentiate a function in implicit form, apply the rules already mentioned and bear in mind that:

x'=1.

In general y'≠1.

Therefore, omit x' and leave y'

Examples

Implicit Function

Implicit Function Differentiation

Implicit Function

Implicit Function Differentiation

When the functions are more complex, there is a rule to facilitate the calculation:

Examples

Implicit Function Example 

Implicit Function Differentiation