Suppose that the functions ƒ and g are defined throughout

Chapter 3, Problem 21AAE

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QUESTION:

Problem 21AAE

Suppose that the functions ƒ and g are defined throughout an open interval containing the point x0 that ƒ is differentiable at  that and that g is continuous at x0. Show that the product ƒg is differentiable at x0. This process shows, for example, that although is not differentiable at x = 0, the product is differentiable at x = 0.

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QUESTION:

Problem 21AAE

Suppose that the functions ƒ and g are defined throughout an open interval containing the point x0 that ƒ is differentiable at  that and that g is continuous at x0. Show that the product ƒg is differentiable at x0. This process shows, for example, that although is not differentiable at x = 0, the product is differentiable at x = 0.

ANSWER:

Solution

Step 1 of 3

In this problem, we have to show that the product of  is differentiable at .

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