Photo by Vickie Kelly, 1993 Greg Kelly, Hanford High School, Richland, Washington 3.8 Derivatives of Inverse Trig Functions Lewis and Clark Caverns, Montana
At x = 2: We can find the inverse function as follows: To find the derivative of the inverse function: Switch x and y.
Slopes are reciprocals. At x = 2: At x = 4:
Slopes are reciprocals. The derivative of Derivative Formula for Inverses: evaluated at the derivative of evaluated at . Because x and y are reversed to find the reciprocal function, the following pattern always holds: is equal to the reciprocal of
Given: Find: Derivative Formula for Inverses: A typical problem using this formula might look like this:
But so is positive. We can use implicit differentiation to find:
We could use the same technique to find and . d - 1 sec x dx
Your calculator contains all six inverse trig functions. However it is occasionally still useful to know the following: p