The product rule allows us to find the derivative of two functions when they are multiplied together. The product rule states that when you have the situation:

Then the derivative is

To prove this, we will take the original functions and apply the definition of a derivative.

The next step is to both add and subtract *f(x + h)g(x)/h. *We can do this because they will cancel each other out and so we can not changing the equation.

Rearranging the equation

Factoring out the *g(x)* from the first two terms and *f(x + h)* from the last two terms.

Using limit properties, we can reformat the equation.

We can again use the definition of a derivative finds:

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