The Product Rule for Derivatives

One of the most often used rules in differential calculus is the product rule.  The product rule is used when you want to find the derivative of a product of two or more functions.  I’ll go over the details in a second, but first take a look at the product rule formula below:

What the product formula above says in plain English is that the derivative of the product of f(x) and g(x) is equal to the derivative of f(x) times g(x) plus the derivative of g(x) times f(x).  Remember the notation f’(x) means the derivative of f(x).

Below is an example where I use the product rule:

Remember from the lesson on derivatives of trig functions that the derivative of sin x is cos x and we know that the derivative of 2x is 2.  So, using those two facts, just apply the product rule where f(x) = 2x, g(x) = sin x, f’(x) = 2, and g’(x) = cos x.

The product rule is used all the time in calculus so if you’re not 100% clear, re-read this post and commit it to memory.  Later on, I’ll show some examples where we can use the product rule on more than 2 functions.

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The Product Rule for Derivatives


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