1. Section 2.5 Implicit Differentiation
Calculus
Section 2.5
Implicit Differentiation

2. 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)

3. 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

4. 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

5. Example

6. Example 2

7. Example 2 continued

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

9. Ex. Cont.

10. Double Derivatives