$\text{f(x)}=$ $-3\cdot \sin \left(x\right)+\frac{9}{2x^4}$

= $-3\cdot \sin \left(x\right)+\frac{9}{2}{x}^{-4}$

=> f'(x) = $-3\cdot \cos \left(x\right)-18x^{-5}$

$\text{f'(x)}=$ $-3\cdot \cos \left(x\right)-\frac{18}{x^5}$

$\text{f(x)}=$ $-\frac{9}{2}\sqrt{x}$

= $-\frac{9}{2}{x}^{\frac{1}{2}}$

=> f'(x) = $-\frac{9}{4}{x}^{-\frac{1}{2}}$

$\text{f'(x)}=$ $-\frac{9}{4\sqrt{x}}$

$\text{f(x)}=$ $-2\sqrt{x}+2x^3$

= $-2x^{\frac{1}{2}}+2x^3$

=> f'(x) = $-x^{-\frac{1}{2}}+6x^2$

$\text{f'(x)}=$ $-\frac{1}{\sqrt{x}}+6x^2$