$\left(c\cdot f\left(x\right)\right){}^{\prime }=c\cdot f{}^{\prime }\left(x\right)$

$\left(x^n\right){}^{\prime }=n{x}^{n-1},n\in \mathbb{Z}$

$\left(\frac{1}{x}\right){}^{\prime }=-\frac{1}{x^2}$

$\left(\sqrt{x}\right){}^{\prime }=\frac{1}{2\sqrt{x}}$

$\left(\sqrt[3]{x}\right){}^{\prime }=\frac{1}{3\sqrt[3]{x^2}}$

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a)

$f{}^{\prime }\left(x\right)=6\cdot 2x=12x$   

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b)

$f{}^{\prime }\left(x\right)=-\frac{2}{3}\cdot 6x^5=-4x^5$   

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c)

$f{}^{\prime }\left(x\right)=\frac{3}{4}\cdot \left(-8\right)x^{-9}=-6x^{-9}$   

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d)

$f{}^{\prime }\left(x\right)=2\cdot \frac{1}{2\sqrt{x}}=\frac{1}{\sqrt{x}}$   

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e)

$f{}^{\prime }\left(x\right)=9\cdot \frac{1}{3\sqrt[3]{x^2}}=\frac{3}{\sqrt[3]{x^2}}$   

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f)

$f{}^{\prime }\left(x\right)=\frac{4}{5}\cdot \frac{1}{2\sqrt{x}}=\frac{2}{5\sqrt{x}}$   

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g)

$f{}^{\prime }\left(x\right)=\sqrt{2}\cdot \left(-\frac{1}{x^2}\right)=-\frac{\sqrt{2}}{x^2}$   

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h)

$f{}^{\prime }\left(x\right)=\left(\frac{1}{0,5x}\right){}^{\prime }=\left(\frac{2}{x}\right){}^{\prime }=2\cdot \left(-\frac{1}{x^2}\right)=-\frac{2}{x^2}$   

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i)

$f{}^{\prime }\left(x\right)=\frac{\pi }{\sqrt{3}}\cdot 2x=\frac{2\pi x}{\sqrt{3}}$