How do you find the first and second derivative of #xlnx^2#?
See below.
First use properties of logarithms to rewrite
Now use the product rule
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To find the first and second derivatives of ( x \ln(x^2) ), you can use the product rule and chain rule.

First derivative: ( f(x) = x \ln(x^2) ) ( f'(x) = 1 \cdot \ln(x^2) + x \cdot \frac{1}{x^2} \cdot 2x ) ( f'(x) = \ln(x^2) + 2 )

Second derivative: ( f'(x) = \ln(x^2) + 2 ) ( f''(x) = \frac{1}{x^2} \cdot 2x + 0 ) ( f''(x) = \frac{2}{x} )
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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