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What is the derivative of #f(x)=ln(e^x+3)# ?

Answer 1

Ezekiel Alexander

#f'(x)=e^x/(e^x+3)#

solution

Let's #y=ln(f(x))#

Differentiating with respect to #x# using Chain Rule, we get,

#y'=1/f(x)*f'(x)#

Similarly following for the given problem yields,

#f'(x)=1/(e^x+3)*e^x#

#f'(x)=e^x/(e^x+3)#

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Answer 2

Emma Aldridge

The derivative of ( f(x) = \ln(e^x + 3) ) is ( \frac{e^x}{e^x + 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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