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Product rule
The product rule gives us a straightforward method to find the derivative of the product of two functions. Let's take two arbitrary functions, f(x) and g(x), and multiply them. So, . The derivative is
.
Let's explore this in more detail to understand how this works. Have a look at the following equation:
![](https://epubservercos.yuewen.com/FF11E0/19470372701459106/epubprivate/OEBPS/Images/Chapter_102.jpg?sign=1738676486-REwVDVD5OVrKQrC2tumQoWP1Jp2hgrdk-0-5383c0121f1b394c9050e77c35c567b6)
We can rewrite the derivative, as follows:
![](https://epubservercos.yuewen.com/FF11E0/19470372701459106/epubprivate/OEBPS/Images/Chapter_896.jpg?sign=1738676486-NrnJkFkYTyNONuXRfgse0XLhXJw6kIBG-0-6e867d6a63c3564f06bcc533f1d9afa4)
This can be further simplified as , which is the same as before.