Product rule

From Simple English Wikipedia, the free encyclopedia

In differential calculus, the product rule is a rule that helps calculate derivates that have multiplication.


Steps[change | change source]

Say we have the function .

The two functions being multiplied are and .

We can set



The rule needs us to find the derivative of both and .

We can find by first using the sum rule to split into and . After using the power rule, we have .

To find , we need to find the derivative of , which is , meaning .

Now we can substitute the values into the equation,


Proof[change | change source]

One definition of a derivative is

, and we're trying to find the derivative of , so we can first set to .

We can't really do much with this so we need to manipulate the equation.

The part is equal to , meaning it didn't change the value of the equation. Now we can factor,

, and because approaches , is equal to .

, and and are just equal to and .



References[change | change source]

  1. "Product rule proof (video) | Optional videos". Khan Academy. Retrieved 2022-09-12.