# How do you differentiate #f(x)=2lnx^3#?

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To differentiate ( f(x) = 2 \ln(x^3) ), you can use the chain rule. The derivative is:

[ f'(x) = \frac{6}{x} ]

Using the chain rule, ( \frac{d}{dx}[\ln(u)] = \frac{1}{u} ) and ( \frac{d}{dx}(x^3) = 3x^2 ). Therefore, ( f'(x) = 2 \cdot \frac{1}{x^3} \cdot 3x^2 = \frac{6}{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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