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## 3.8 Derivatives of Inverse Trig Functions

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**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