Table of contents

### Premise

In calculus, more often than not, we have to differentiate functions which are a product of two or more functions.

In a mathematical format this looks like:

For example:

or sometimes a product of multiple functions:

For example:

which by a simple substitution can be turned into a product of 2 functions:

### Solution

The derivative of a product of two functions is the following:

### Derivation

We start from basic principles, the definition of a derivative:

Now, using the product property of limits, we have:

Which turns into:

that finally leads to the product rule:

### About Vincenzo Barbato

*Known to his friends as Enzo, he's an outside-the-box engineer/researcher whose interests and expertise span many fields, including controls systems, multi-physics simulations, mechatronics, oil technologies, data analysis and machine vision just to name a few.*

*Refusing to grow up, he's on a continuous journey to develop simple and creative solutions that have the power of disrupting industries by optimizing systems and processes.*

*Married to a beautiful wife, with two beautiful daughters and two identical twin boys, his home is a never ending chaotic fountain of inspiration.*

*His outlook on life: *

"Never blindly accept what you're told, listen, but then question, with curiosity, creativity and collaboration we can change the world"

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