derivative of 2\sqrt[3]{x}-7/(sqrt(x))

Lösung

\frac{d}{d x} (2 3 x - \frac{7}{x})

\frac{2}{3 x ^{\frac{2}{3}}} + \frac{7}{2 x ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (2 3 x - \frac{7}{x})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (2 3 x) - \frac{d}{d x} (\frac{7}{x})

\frac{d}{d x} (2 3 x) = \frac{2}{3 x ^{\frac{2}{3}}}

\frac{d}{d x} (\frac{7}{x}) = - \frac{7}{2 x ^{\frac{3}{2}}}

= \frac{2}{3 x ^{\frac{2}{3}}} - (- \frac{7}{2 x ^{\frac{3}{2}}})

Vereinfache

= \frac{2}{3 x ^{\frac{2}{3}}} + \frac{7}{2 x ^{\frac{3}{2}}}

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