# 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?

##### 2 Answers

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False

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Take

then

then

But

It must be

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#### Answer:

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) #

#### Explanation:

We can readily disprove the given statement:

Consider:

#f(x)=x# and#g(x)=x#

Then differentiating wrt

#f'(x)=1# and#g'(x)=1 => f'(x)g'(x)=1#

And

And so By counterexample, the statement is **false** .

In fact the product rule provides the correct formulation:

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

Describe your changes (optional) 200