# How do you differentiate #f(x)=ln (x^3+3)#?

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To differentiate the function ( f(x) = \ln(x^3 + 3) ), you would apply the chain rule.

[ \frac{d}{dx}(\ln(u)) = \frac{1}{u} \cdot \frac{du}{dx} ]

Where ( u = x^3 + 3 ).

Now, differentiate ( u ) with respect to ( x ):

[ \frac{du}{dx} = \frac{d}{dx}(x^3 + 3) = 3x^2 ]

Finally, substitute ( u ) and ( \frac{du}{dx} ) into the chain rule formula:

[ \frac{d}{dx}(\ln(x^3 + 3)) = \frac{1}{x^3 + 3} \cdot 3x^2 = \frac{3x^2}{x^3 + 3} ]

So, the derivative of ( f(x) ) is ( \frac{3x^2}{x^3 + 3} ).

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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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