1. Derivatives of Inverse Trig Functions
AP Calculus AB
Derivatives of Inverse Trig Functions

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. Example 1
Find the derivative of y with respect to the appropriate variable of:
We will need to use the product rule on the first term and the chain rule on the second term.
Bam!

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

10. Example 2
Find the derivative of y with respect to the appropriate variable of:

11. Example 1 (cont.)

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