Power rule

The power rule helps to find the derivative of a function where the variable has an exponent. Simply put, you multiply the power by the constant in front of the variable, and reduce the power by 1. Let's see what an example of this looks like, using the power rule , as follows:

There are certain functions—such as  or  —that are not as straightforward as the ones we saw earlier. The function  is not differentiable at x = 0 because its value is undefined. This is known as discontinuity.

The same applies to ; however, e (known as Euler's number) has a very interesting property whereby the function is equal to its derivative—that is, .