The product rule states that if h(x) = f(x)g(x) then h'(x) = f'(x)g(x) + f(x)g'(x).  In other words if a function is made by multiplying two functions, say the first function and the second function, the derivative of the new function equals the derivative of the first function times the second function + the derivative of the second function time the first function. For example the derivative of (3x^2)(5x^3) is 6x(5x^3) + (3x^2)(15x^2). From ch 4.1 we know tha the derivative of 3x^2 = 6x. 1.   How could you use  the power rule to take the derivative of 3x^2 ?  2.   Do you get the same answer? 3.   Which is the easiest way to do this derivative, the power rule or the product rule ?

Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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The product rule states that if h(x) = f(x)g(x) then h'(x) = f'(x)g(x) + f(x)g'(x).  In other words if a function is made by multiplying two functions, say the first function and the second function, the derivative of the new function equals the derivative of the first function times the second function + the derivative of the second function time the first function.

For example the derivative of (3x^2)(5x^3) is 6x(5x^3) + (3x^2)(15x^2).

From ch 4.1 we know tha the derivative of 3x^2 = 6x.

1.   How could you use  the power rule to take the derivative of 3x^2 ? 

2.   Do you get the same answer?

3.   Which is the easiest way to do this derivative, the power rule or the product rule ? 

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