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How do I find the derivative of #f(x)=ln (x^3+3)#?

Answer 1

Charles Arocha

Using chain rule, which states that #(dy)/(dx)=(dy)/(du)(du)/(dx)#

Renaming #u=x^3+3#, we can differentiate it now, as #f(x)ln(u)#

#(dy)/(dx)=1/u(3x^2)=(3x^2)/(x^3+3)#

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Answer 2

Isabella Ackerman

To find the derivative of ( f(x) = \ln(x^3 + 3) ), use the chain rule: [ f'(x) = \frac{1}{x^3 + 3} \cdot \frac{d}{dx}(x^3 + 3) = \frac{1}{x^3 + 3} \cdot 3x^2 = \frac{3x^2}{x^3 + 3} ]

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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.

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