# Thread: derivative of ln

1. ## derivative of ln

im currently trying to find the derivative of
f(x)= ln[x+(4+x²)^(1/2)]
im a little confused on how to approach this...any help would be greatly appreciated for get me started! thx
ln(x) + [1/2]ln(4+x²) is incorrect right?

2. Originally Posted by nuclear123
im currently trying to find the derivative of
f(x)= ln[x+(4+x²)^(1/2)]
im a little confused on how to approach this...any help would be greatly appreciated for get me started! thx
ln(x) + [1/2]ln(4+x²) is incorrect right?

in general

$\displaystyle f = ln g$

$\displaystyle f ' = \frac{g'}{g}$

$\displaystyle f(x) = \ln (x+(4+x^2)^{\frac{1}{2}})$

let

$\displaystyle g(x) = x + (4+x^2)^{\frac{1}{2}}$

$\displaystyle f(x) = \ln g(x)$ so $\displaystyle f'(x) = \frac{g'(x)}{g(x)}$

first find
$\displaystyle g'(x) = 1 + \frac{1}{2} (2x) (4+x^2)^\frac{-1}{2}$

so

$\displaystyle f'(x) = \frac{g'(x)}{g(x)} = \frac{1 + \frac{1}{2} (2x) (4+x^2)^\frac{-1}{2}}{x + (4+x^2)^{\frac{1}{2}}}$

simplify it