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

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Presentation transcript:

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

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

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

A typical problem using this formula might look like this: Given: Find: Derivative Formula for Inverses:

We can use implicit differentiation to find:

But so is positive.

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

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