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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=1739694861-4jyJJpb6iCcRyBFP3yN37WB1yJVtLuqQ-0-6786d9be4b1ec30dcff1adc3eea274df)
We can rewrite the derivative, as follows:
![](https://epubservercos.yuewen.com/FF11E0/19470372701459106/epubprivate/OEBPS/Images/Chapter_896.jpg?sign=1739694861-RLmqzatsY09VIwZ0CrQbHIVqdd48tjJw-0-f1419c9a07e217b496fab43e08ed1c09)
This can be further simplified as , which is the same as before.