Answer
The derivative is $\frac{-5}{4x^4}-2sin(x)$.
Work Step by Step
This question requires you to use every trick you've used till now. The overall derivative is the sum of the derivatives of the mini functions. $\frac{5}{8x^3}$ can be rewritten as $\frac{5x^{-3}}{8}$ whose derivative is $\frac{-4*5x^{-4}}{8}$ which simplifies to $\frac{-5}{4x^4}$. The second part of the question is since the derivative of $cos(x)$ is $-sin(x)$, hence the derivative of $2cos(x)$ is $-2sin(x)$. The overall derivative then is $\frac{-5}{4x^4}-2sin(x)$.
