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