derivative of \sqrt[3]{5x}+4x^{1/2}-3x

Lösung

\frac{d}{d x} (3 5 x + 4 x^{\frac{1}{2}} - 3 x)

\frac{5 ^{\frac{1}{3}}}{3 x ^{\frac{2}{3}}} + \frac{2}{x ^{\frac{1}{2}}} - 3

Schritte zur Lösung

\frac{d}{d x} (3 5 x + 4 x^{\frac{1}{2}} - 3 x)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (3 5 x) + \frac{d}{d x} (4 x^{\frac{1}{2}}) - \frac{d}{d x} (3 x)

\frac{d}{d x} (3 5 x) = \frac{5 ^{\frac{1}{3}}}{3 x ^{\frac{2}{3}}}

\frac{d}{d x} (4 x^{\frac{1}{2}}) = \frac{2}{x ^{\frac{1}{2}}}

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

= \frac{5 ^{\frac{1}{3}}}{3 x ^{\frac{2}{3}}} + \frac{2}{x ^{\frac{1}{2}}} - 3

\frac{d}{d x} (2 x ln (4 x^{2}))

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