1. 13. 2 Derivatives of functions given parametrically
13.2 Derivatives of functions given parametrically. Tangent Lines and Arc Lengths
Rita Korsunsky

2. of function given parametrically
Derivative
of function given parametrically
by x=f(t) and y= g(t)
By the Chain Rule:

3. Example 1

4. Slope of the tangent line

5. Example 2

6. Example 3

7. Example 4
Solution: or

8. Example 4, continued
Solution:
and

10. Example 5

11. Example 6

12. Example 6, continued From part (a):
function k that has the same graph as C
in agreement with part (b)

13. Let’s prove it !
Theorem:

14. Proof:
Remember?

15. Example 7
Solution:
link

16. Example 8 + -