Section 2.5 Implicit Differentiation Calculus Section 2.5 Implicit Differentiation

Terminology Equations in explicit form can be solved for y in terms of x (e.g. functions) Equations in implicit form CANNOT be solved for y in terms of x (e.g. equations of circles)

Implicit Differentiation Goal is to find (to derive with respect to x) Differentiate x terms as usual (apply Power Rule, etc.) Differentiate y terms, applying the Chain Rule

Implicit Differentiation Process Differentiate both sides of the equation with respect to x Move all terms to the left side, and all other terms to the right side Factor out from the left side Solve for , by dividing

Example

Example 2

Example 2 continued

Example We want the derivative in terms of x and y, so substitute for dy/dx

Ex. Cont.

Double Derivatives