# How do you find the derivative of #x ln (x) - x#?

Knowing the product rule for derivatives, which tells us that

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To find the derivative of ( x \ln(x) - x ), you can use the product rule along with the derivative of ( \ln(x) ) which is ( \frac{1}{x} ). Applying the product rule, the derivative is:

[ \frac{d}{dx} (x \ln(x) - x) = \frac{d}{dx} (x \ln(x)) - \frac{d}{dx} (x) ]

[ = \left(\ln(x) + \frac{1}{x}\right) \cdot x - 1 ]

[ = \ln(x) + 1 - 1 ]

[ = \ln(x) ]

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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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