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a)
-\frac{2}{\sqrt{x}}{,}\ x>0
D\left(-2x^{-\frac{1}{2}}\right)=-2\cdot\left(-\frac{1}{2}\right)x^{-\frac{3}{2}}=x^{-\frac{3}{2}}
b)
\sqrt[3]{x^2}=x^{\frac{2}{3}}
D\left(x^{\frac{2}{3}}\right)=\frac{2}{3}x^{-\frac{1}{3}}=\frac{2}{3\sqrt[3]{x}}
c)
 
\frac{x^2}{3\sqrt{x}}=\frac{1}{3}x^2\cdot x^{-\frac{1}{2}}
D\left(f\left(x\right)g\left(x\right)\right)=f'\left(x\right)g\left(x\right)+f\left(x\right)g'\left(x\right)
f\left(x\right)=x^2
f'\left(x\right)=2x
g\left(x\right)=x^{-\frac{1}{2}}
g'\left(x\right)=-\frac{1}{2}x^{-\frac{3}{2}}
D\left(\frac{1}{3}x^2x^{-\frac{1}{2}}\right)=2x\cdot x^{-\frac{1}{2}}+x^2\cdot\left(-\frac{1}{2}x^{-\frac{3}{2}}\right)=2x^{-\frac{1}{2}}-\frac{1}{2}x^{-3}=\frac{2}{\sqrt{x}}-\frac{1}{2x^3}