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

1 Answer
Jul 31, 2014

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.