Question

Derivative of a natural log function?? Answer provided
Find the derivative:
f(x) = ln(sqrt(4+x^2)/x)
The answer is supposed to be -4/(x(x^2+4))

Answer 1

\(\sqrt A = A^{1/2}\)
use this, so that you can use the property of log,
\(\log A^B = B \log A\)
which would simplify your expression.

Answer 2

Given \(\ln u(x)\), you have \(\dfrac{d}{dx}[\ln u(x)]=\dfrac{\frac{d}{dx}[u(x)]}{u(x)}\)