Home > Calculus > Differentiating Logarithmic Functions with Base e

What is the derivative of #f(x)=ln(x^2+x)# ?

Answer 1

Samantha Adkison

We find the derivative by using the chain rule.

#f(x)=ln(x^2+x)#

#f'(x)=1/(x^2+x)*(x^2+x)'#

#f'(x)=1/(x^2+x)*(2x+1)#

#f'(x)=(2x+1)/(x^2+x)#

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Answer 2

Emily Ammerman

The derivative of ( f(x) = \ln(x^2 + x) ) is ( \frac{d}{dx} \ln(x^2 + x) = \frac{2x + 1}{x^2 + 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.

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