1. Lesson 3-8: Derivatives of Inverse Trig Functions
AP Calculus
Mrs. Mongold

2. At x = 2:
We can find the inverse function as follows:
To find the derivative of the inverse function:
Switch x and y.

3. Slopes are reciprocals.
At x = 2:
At x = 4:

4. Slopes are reciprocals.
Because x and y are reversed to find the reciprocal function, the following pattern always holds:
The derivative of
Derivative Formula for Inverses:
evaluated at
is equal to the reciprocal of
the derivative of
evaluated at

5. A typical problem using this formula might look like this:
Given:
Find:
Derivative Formula for Inverses:

6. We can use implicit differentiation to find:

7. We can use implicit differentiation to find:
But
so is positive.

8. We could use the same technique to find and. 1
sec d x dx -

9. Your calculator contains all six inverse trig functions.
However it is occasionally still useful to know the following:

10. Example
Differentiate y = sin-1x2

11. Example
A particle moves a long the x-axis so that its position at any time t>0 is x(t)=tan what is the velocity of the particle when t = 16?

12. Example
Differentiate y = sec-1 (5x4)

13. Homework
Page /1-17 odd, 19-21, 23-26 p