The technique of implicit differentiation allows you to find the derivative of y with respect to x without having to solve the given equation for y. The chain rule must be used whenever the function y is being differentiated because of our assumption that y may be expressed as a function of x.

Why is implicit differentiation important?

Implicit differentiation is the special case of related rates where one of the variables is time. Implicit differentiation has an important application: it allows to compute the derivatives of inverse functions. It is good that we review this, because we can use these derivatives to find anti-derivatives.

What is the big idea of implicit differentiation?

Implicit differentiation allows us to find slopes of tangents to curves that are clearly not functions (they fail the vertical line test). We are using the idea that portions of y are functions that satisfy the given equation, but that y is not actually a function of x.