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

Answer 1

I'll assume that by #log# you meant a logarithm with base 10. Shouldn't be an issue anyways since the logic applies to other bases as well.

First we will apply the change-of-base rule:

#f(x) = y = ln(x^2 + x)/ln(10)#

We can consider #1/ln10# to just be a constant, so take the derivative of the numerator and apply the chain rule:

#dy/dx = 1/ln(10) * 1/(x^2 + x) * (2x + 1)#

Simplify a bit:

#dy/dx = (2x + 1)/(ln(10)*(x^2 + x))#

There's our derivative. Keep in mind, taking derivatives of logarithms without base #e# is just a matter of using change-of-base rule to convert them to natural logarithms, which are easy to differentiate.

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Answer 2

Adam Adkins

To find the derivative of ( f(x) = \log(x^2 + x) ), you would use the chain rule and the derivative of the natural logarithm function. Applying the chain rule, the derivative is ( f'(x) = \frac{1}{x^2+x}(2x+1) ).

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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.