Derivative of a product of functions
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:
or sometimes a product of multiple functions:
which by a simple substitution can be turned into a product of 2 functions:
The derivative of a product of two functions is the following:
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:
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