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

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

Example 1

Slope of the tangent line

Example 2

Example 3

Example 4 Solution: or

Example 4, continued Solution: and

Example 5

Example 6

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

Let’s prove it ! Theorem:

Proof: Remember?

Example 7 Solution: link

Example 8 + -