Determine the first, second, and third derivatives of the function $g\left(x\right)=4x^3+7e^x$.

Calculate the fourth derivative of the function $f\left(x\right)=5\cos x$.

By examining the pattern of derivatives, determine the $\text{500th}$ derivative of $7\cos \left(3x\right)$.

Determine the second derivative of $y={(2+\sqrt{x})}^{-1}$.