# How do you differentiate #f(x)=xsin(1/x)#?

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To differentiate the function ( f(x) = x \sin\left(\frac{1}{x}\right) ), you would use the product rule. The derivative is given by:

[ f'(x) = x \cos\left(\frac{1}{x}\right) - \frac{\sin\left(\frac{1}{x}\right)}{x^2} ]

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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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