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

= $5x^{-2}$

=> f'(x) = $-10x^{-3}$

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

$\text{f(x)}=$ $\frac{5}{3}{x}^3-6\sqrt[3]{x}$

= $\frac{5}{3}{x}^3-6x^{\frac{1}{3}}$

=> f'(x) = $5x^2-2x^{-\frac{2}{3}}$

$\text{f'(x)}=$ $5x^2-\frac{2}{{\left(\sqrt[3]{x}\right)}^2}$

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

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

=> f'(x) = $-12x^{-5}-2\cdot \cos \left(x\right)$

$\text{f'(x)}=$ $-\frac{12}{x^5}-2\cdot \cos \left(x\right)$