product rule
(a^m)(a^n) = a^m+nWhen multiplying 2 like bases, add the exponents
The product rule is a formula used in calculus that allows us to find the derivative of the product of two functions. It is often stated as follows:
If f(x) and g(x) are functions of x, then the derivative of their product, f(x)g(x), is given by:
(fg)'(x) = f'(x)g(x) + f(x)g'(x)
In other words, to find the derivative of the product of two functions, we differentiate the first function and leave the second one alone, and then add to it the product of the first function and the derivative of the second function.
This formula can be very useful when dealing with more complicated functions that can be broken down into products of simpler functions. It is also important to remember that the product rule only applies when differentiating products of functions, and we need to use other rules (such as the chain rule or quotient rule) for other types of functions.
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