derivative of \sqrt[7]{x}+6sqrt(x^7)

Lösung

\frac{d}{d x} (7 x + 6 x^{7})

\frac{1 + 147 x ^{\frac{47}{14}}}{7 x ^{\frac{6}{7}}}

Schritte zur Lösung

\frac{d}{d x} (7 x + 6 x^{7})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (7 x) + \frac{d}{d x} (6 x^{7})

\frac{d}{d x} (7 x) = \frac{1}{7 x ^{\frac{6}{7}}}

\frac{d}{d x} (6 x^{7}) = 21 x^{\frac{5}{2}}

= \frac{1}{7 x ^{\frac{6}{7}}} + 21 x^{\frac{5}{2}}

Vereinfache

\frac{1}{7 x ^{\frac{6}{7}}} + 21 x^{\frac{5}{2}} : \frac{1 + 147 x ^{\frac{47}{14}}}{7 x ^{\frac{6}{7}}}

= \frac{1 + 147 x ^{\frac{47}{14}}}{7 x ^{\frac{6}{7}}}

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