Product Rule

Videos

$Product Rule Example 1$

$Product Rule Example 2$

$Product Rule Example 3$

PJ Chain Rule + Product Rule + Factoring

PJ Chain Rule + Product Rule + Simplifying – Ex 1

PJ Chain Rule + Product Rule + Simplifying – Ex 2

Worksheets

$Product Rule Worksheet Example 1$

Whenever a function is comprised of two separate functions, you’ll have to use Product Rule in order to take its derivative. For example, if your function is $f(x)=2xe^x$ , you should recognize that it’s comprised of two functions, $2x$ , and $e^x$ , which are multiplied together. In order to take the derivative of this function, you’ll have to use Product Rule. Considering the formula below, you’ll treat the first function, $2x$ , as $f(x)$ , and the second function, $e^x$ , as $g(x)$ .

$\frac{d}{dx}(f(x))\cdot (g(x))=(f'(x)\cdot g(x))+(f(x)\cdot g'(x))$

Finding the derivative of a function like this, means that we’ll take the derivative of the first function, multiply it by the second function, then add to that the derivative of the second function, multiplied by the first function.

Let’s look at the example we mentioned above in more detail.

Example

Find the derivative of $h(x)= 2xe^x$ .

According the formula of the Product Rule, we’ll treat $2x$ as $f(x)$ and we’ll treat $e^x$ as $g(x)$ . We’ll find the derivative of $f(x)$ and $g(x)$ separately, and then plug both functions and their derivatives into our Product Rule formula.

$f(x)=2x$ $g(x)=e^x$