2. DIFFERENTIAL CALCULUS IMPLICIT DIFFERENTIATION

4. EXAMPLE NO. 1

5. differentiating the formula of circle differentiate both sides * note the use of chain rule

6. differentiating the formula of circle

7. EXAMPLE NO. 2

8. differentiation of trigonometric functions

9. EXAMPLE NO. 3

10. application to tangents and normals Find the equations of the lines at (-1 , 2) tangent and normal to the curve Find :

11. application to tangents and normals Find the equations of the lines at (-1 , 2) tangent and normal to the curve tangent : normal: recall: m = -1/m for normal

12. EXAMPLE NO. 4

13. higher order derivative Find if .

14. higher order derivative substitute y’ in the equation Find if .

15. -end- this was made by rainiee mar.4,2008 submitted to: Engr. Robert Canda