When you have to take the derivative of 2 variables being multiplied, we use the
product rule. If we have f(x)g(x), the derivative will be:
(f(x)g(x))' = f(x)g'(x) + g(x)f'(x).
Now, the primes can be a little confusing when you are learning how to apply this for the first time, so lets denote the number 1 to f(x) and the number 2 to g(x), where 1 refers...
Rules for Differentiation
Here is a list of general rules that can be applied when finding the derivative of a function. These properties are mostly derived from the
limit definition of the derivative.
see product rule
see quotient rule
see chain rule
Product Rule Explanation
It is not always necessary to compute
derivatives directly from the definition. Several rules have been developed for finding the derivatives without having to use the definition directly. These rules simplify the process of differentiation. The Product Rule is a formula developed by Leibniz used to find the derivatives of products of functions.