Answer
$f'(t)=(\frac{1}{2ln2})(\frac{3 (\sqrt t) ln(t+1)}{2}+\frac{t \sqrt t}{t+1})$
Work Step by Step
$f(t)=t^{\frac{3}{2}} \frac{ln(t+1)^{\frac{1}{2}}}{ln2}$
$=\frac{t^{\frac{3}{2}}(\frac{1}{2})ln(t+1)}{ln2}$
$f(t)=\frac{1}{2ln2}(t^{\frac{3}{2}})ln(t+1)$
let
$u=t^{\frac{3}{2}}$
$u'=\frac{3t^{\frac{1}{2}}}{2}$
$v=ln(t+1)$
$v'=\frac{1}{t+1}$
$f'(t)=(\frac{1}{2ln2})(\frac{3 (\sqrt t) ln(t+1)}{2}+\frac{t \sqrt t}{t+1})$
