How do you find the derivative of the product of two functionsthat are differentiable at a point?

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.1: Techniques For Finding Derivatives
Problem 8E: Find the derivative of each function defined as follows. y=-100x-11x2/3
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How do you find the derivative of the product of two functions
that are differentiable at a point?

Expert Solution
Step 1

Consider the two functions f(x) and g(x).

f(x)·g(x)'=f'(x)g(x)+g'(x)f(x). Here f(x)·g(x)' represents the derivative of product of two function, f'(x) represents the derivative of f(x) and g'(x) represents the derivative of g(x).

 

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