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

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

=> f'(x) = $-12x^{-4}+5\cdot \cos \left(x\right)$

$\text{f'(x)}=$ $-\frac{12}{x^4}+5\cdot \cos \left(x\right)$

$\text{f(x)}=$ $\frac{5}{4}\sqrt{x}$

= $\frac{5}{4}{x}^{\frac{1}{2}}$

=> f'(x) = $\frac{5}{8}{x}^{-\frac{1}{2}}$

$\text{f'(x)}=$ $\frac{5}{8\sqrt{x}}$

$\text{f(x)}=$ $4x^4+5$

$\text{f'(x)}=$ $16x^3+0$

= $16x^3$