Finding Tangent Slopes from Implicit Equations

Implicit differentiation with partial derivatives helps find tangent slopes when two variables are linked by one equation. The relationship is not solved for one variable first. Instead, both variables stay connected in the same implicit relation.

To work with this kind of equation, one variable ...

Consider a function F of x and y, and suppose it is equal to zero, where y is defined implicitly as a function of x.

To find the derivative of the function without isolating y, the chain rule is applied to the entire identity.

This operation produces the partial derivative of F with re...