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

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. If I have seen farther than others, it is because I was standing on the shoulders of giants. -- Isaac Newton
If I have not seen as far as others, it is because giants were standing on my shoulders. -- Hal Abelson