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Beliebt Rechnen >

derivative \sqrt[4]{x}+1/(x^4)

Lösung

ableitung von

4 x + \frac{1}{x ^{4}}

Lösung

\frac{x ^{5} - 16 x ^{\frac{3}{4}}}{4 x ^{\frac{23}{4}}}

Schritte zur Lösung

\frac{d}{d x} (4 x + \frac{1}{x ^{4}})

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (4 x) = \frac{1}{4 x ^{\frac{3}{4}}}

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

= \frac{1}{4 x ^{\frac{3}{4}}} - \frac{4}{x ^{5}}

Vereinfache

\frac{1}{4 x ^{\frac{3}{4}}} - \frac{4}{x ^{5}} : \frac{x ^{5} - 16 x ^{\frac{3}{4}}}{4 x ^{\frac{23}{4}}}

= \frac{x ^{5} - 16 x ^{\frac{3}{4}}}{4 x ^{\frac{23}{4}}}

Graph

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