Answer
$$G'(t)=\frac{\sqrt 5}{2\sqrt t}-\frac{\sqrt7}{t^2}$$
Work Step by Step
$$G(t)=\sqrt{5t}+\frac{\sqrt7}{t}$$$$G(t)=\sqrt5t^{1/2}+\sqrt7t^{-1}$$
So, $$G'(t)=\sqrt5\frac{d}{dt}(t^{1/2})+\sqrt7\frac{d}{dt}(t^{-1})$$
$$G'(t)=\sqrt5\times\frac{1}{2}\times t^{-1/2}+\sqrt7\times(-1)\times t^{-2}$$
$$G'(t)=\frac{\sqrt5}{2}\times\frac{1}{\sqrt t}-\sqrt 7\times\frac{1}{t^2}$$
$$G'(t)=\frac{\sqrt 5}{2\sqrt t}-\frac{\sqrt7}{t^2}$$
