# How do you find the derivative of #x^2 lnx#?

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To find the derivative of (x^2 \ln(x)), you use the product rule. The product rule states that if you have two functions (u(x)) and (v(x)), then the derivative of their product is (u'(x)v(x) + u(x)v'(x)). Applying this to (x^2) and (\ln(x)), where (u(x) = x^2) and (v(x) = \ln(x)), the derivative is:

[ \frac{d}{dx}(x^2 \ln(x)) = (2x \cdot \ln(x)) + (x^2 \cdot \frac{1}{x}) ]

Simplifying this expression gives:

[ 2x \ln(x) + 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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