With the rules we have at our disposal so far, we cannot calculate some types of derivatives.

We will now see the **chain rule**, a formula for the derivative of the function composed of two functions. Created by Gottfried Leibniz, the*chain rule* was of great importance for the advancement of differential calculus.

The formula is as follows:

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It can be written as:

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Another similar formula is as follows:

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Calculate

We proceed as follows:

We write y = *ln* (x² + 1). Hoping to use the derivative of* ln*we will do:

u = x² + 1

y =* ln* u

We calculate:

We use the **chain rule**, whose first member is the derived derivative:

ie multiplying the derivatives obtained in the previous step:

We now use the expression of **u** which is (x² + 1), to obtain

## Inverse Function Derivative

The inverse of the function *y*(*x*) is the function *x*(*y*):

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