Finding the Derivative of an Inverse Function

In our studies of differential calculus, we have discovered the derivatives for a number of familiar functions. For invertible functions, it can often be the case that we know the derivative of the function, but not its inverse.

It would be of great help if we could use the close relationship between a function and its inverse to find the derivative of the inverse function. It turns out that we can in fact do this, and the relationship between the two derivatives is rather straightfoward

\frac{dx}{dy} = \frac1{\frac{dy}{dx}}

We will see that there are some complexities in the application of this seemingly simple equation, but in spite of this we will see how we can easily calculate the derivatives of some new functions.

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