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Beliebt Rechnen >

derivative of \sqrt[4]{5/4 x}

Lösung

\frac{d}{d x} (4 \frac{5}{4} x)

Lösung

\frac{5 ^{\frac{1}{4}}}{4 2 x ^{\frac{3}{4}}}

Schritte zur Lösung

\frac{d}{d x} (4 \frac{5}{4} x)

Wende die Kettenregel an:

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

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

\frac{d}{d x} (\frac{5}{4} x) = \frac{5}{4}

= \frac{1}{4 ( \frac{5}{4} x ) ^{\frac{3}{4}}} \cdot \frac{5}{4}

Vereinfache

\frac{1}{4 ( \frac{5}{4} x ) ^{\frac{3}{4}}} \cdot \frac{5}{4} : \frac{5 ^{\frac{1}{4}}}{4 2 x ^{\frac{3}{4}}}

= \frac{5 ^{\frac{1}{4}}}{4 2 x ^{\frac{3}{4}}}

Graph

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