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.

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:

We can use implicit differentiation to find:

But

so is positive.

We could use the same technique to find and

.1sec

dx

dx-

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

p