$\text{f(x)}=$ $-3\cdot \cos \left(x\right)+\frac{4}{x^3}$

= $-3\cdot \cos \left(x\right)+4x^{-3}$

=> f'(x) = $3\cdot \sin \left(x\right)-12x^{-4}$

$\text{f'(x)}=$ $3\cdot \sin \left(x\right)-\frac{12}{x^4}$

$\text{f(x)}=$ $x^5+2\sqrt{x}$

= $x^5+2x^{\frac{1}{2}}$

=> f'(x) = $5x^4+x^{-\frac{1}{2}}$

$\text{f'(x)}=$ $5x^4+\frac{1}{\sqrt{x}}$

$\text{f(x)}=$ $-\frac{5}{2x^3}-4\cdot \sin \left(x\right)$

= $-\frac{5}{2}{x}^{-3}-4\cdot \sin \left(x\right)$

=> f'(x) = $\frac{15}{2}{x}^{-4}-4\cdot \cos \left(x\right)$

$\text{f'(x)}=$ $\frac{15}{2x^4}-4\cdot \cos \left(x\right)$