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a)
f\left(x\right)=4\sqrt{x}{,}\ x>0
f\left(x\right)=4x^{\frac{1}{2}}
f'\left(x\right)=4\cdot\frac{1}{2}\cdot x^{\frac{1}{2}-1}=2x^{-\frac{1}{2}}=\frac{2}{\sqrt{x}}
b)
f\left(x\right)=x^2\sqrt{x}=x^2x^{\frac{1}{2}}
f'\left(x\right)=\frac{5}{2}x^{\frac{3}{2}}
c)
f\left(x\right)=\frac{6}{\sqrt{x}}=6x^{-\frac{1}{2}}
f'\left(x\right)=6\cdot\left(-\frac{1}{2}\right)\cdot x^{-\frac{1}{2}-1}=-3x^{-\frac{3}{2}}