# If y = f(x)g(x), then dy/dx = f‘(x)g‘(x). If it is true, explain your answer. If false, provide a counterexample. True or False?

False

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The statement is false .

The product rule provides the correct formulation:

#y = f(x)g(x) => y = f(x)g'(x) + f'(x)g(x) #

We can readily disprove the given statement:

Consider:

And so By counterexample, the statement is false .

In fact the product rule provides the correct formulation:

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False. The correct formula for the product rule is ( \frac{{dy}}{{dx}} = f'(x)g(x) + f(x)g'(x) ). This rule states that when differentiating the product of two functions, ( f(x) ) and ( g(x) ), with respect to ( x ), the result is the derivative of the first function times the second function, plus the first function times the derivative of the second function.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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