Find the derivative Find the second derivative Warm-up Find the derivative Find the second derivative

16. Section 3.9 Derivatives of Inverse Functions

Derivatives of Inverse Functions EQ – How do you find the derivative of an inverse function?

Derivative of an inverse function If f(x) is a function and g(x) is its inverse, Steps Find the inverse (g(x)) Find f’(x) Plug inverse in for x in f’(x)

Example Find g’(x) if f(x) = x2 + 4

Derivatives of Inverse Trig Functions Using the method we used before, we can come up with equations for derivatives of inverse trig functions

Example Calculate f’(1/2) where f(x) = arcsin(x2) (remember arcsin is another notation for sin-1) (You need to use chain rule)

The rest of inverse trig functions

Example Calculate f’(x) where f(x) = tan-1(3x+1)

Example Find when x = 0

Assignment Pg. 191: #1-7 odd, 19-33 odd