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

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

=> f'(x) = $-8x^{-3}+\frac{5}{3}\cdot \cos \left(x\right)$

$\text{f'(x)}=$ $-\frac{8}{x^3}+\frac{5}{3}\cdot \cos \left(x\right)$

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

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

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

$\text{f'(x)}=$ $\frac{1}{\sqrt{x}}$

$\text{f(x)}=$ $2x^5-\frac{4}{9}{x}^3$

$\text{f'(x)}=$ $10x^4-\frac{4}{3}{x}^2$