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

Answer 1
#f(x)=2lnx^3# Can be differentiated by using the chain rule We'll go through that that after we do it the easy way.
Use the fact the #ln a^p = p lna# to rewrite the function:
#f(x)=2lnx^3=2(3lnx)=6 lnx#.
And so, #f'(x)=6*1/x=6/x#.

OR

#f(x)=2lnx^3#
#f'(x)=2[1/x^3*3x^2]=(6x^2)/x^3 = 6/x#.
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Answer 2

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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Answer from HIX Tutor

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.

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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