Question

derive a função!
$R(x)= \frac{ \sqrt{10} }{ x^{3} }$

$f(t)= \sqrt{t}- \frac{1}{ \sqrt{t} }$

Answer 1

$R(x) = \sqrt{10} x^{-3} =\ \textgreater \ \boxed{R' = -3x^{-4}\sqrt{10}} \\\\ f(t) = \sqrt{t} - \frac{1}{ \sqrt{t} } = t^{ \frac{1}{2} } - t^{- \frac{1}{2} } =\ \textgreater \ \\\\ f' = \frac{1}{2}t^{- \frac{1}{2} } - ( -\frac{1}{2} )t^{- \frac{3}{2} }=\\\\ \boxed{f' = \frac{1}{2 \sqrt{t} } + \frac{1}{2 \sqrt[2]{t^{3}} } }$