#### Answer

$G'(t)=\dfrac{\sqrt{5}}{2\sqrt{t}}-\dfrac{\sqrt{7}}{t^{2}}$

#### Work Step by Step

Rewrite the function
$G(t)=\sqrt{5}t^{1/2}+\sqrt{7}t^{-1}$
Derivate apply power rule
$G'(t)=\dfrac{\sqrt{5}}{2}t^{-1/2}-\sqrt{7}t^{-2}$
$G'(t)=\dfrac{\sqrt{5}}{2\sqrt{t}}-\dfrac{\sqrt{7}}{t^{2}}$