Hands-On Mathematics for Deep Learning

Product rule

The product rule gives us a straightforward method to find the derivative of the product of two functions. Let's take two arbitrary functions, f(x) and g(x), and multiply them. So, . The derivative is .

Let's explore this in more detail to understand how this works. Have a look at the following equation:

We can rewrite the derivative, as follows:

This can be further simplified as , which is the same as before.