1. 3.8 Derivatives of Inverse Trig Functions Lewis and Clark Caverns, Montana Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 1993

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

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

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

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. 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: 