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Beliebt Rechnen >

derivative of e^{\sqrt[4]{x-1}}

Lösung

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

Lösung

\frac{e ^{4 x - 1}}{4 ( x - 1 ) ^{\frac{3}{4}}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

e^{4 x - 1} \frac{1}{4 ( x - 1 ) ^{\frac{3}{4}}} : \frac{e ^{4 x - 1}}{4 ( x - 1 ) ^{\frac{3}{4}}}

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

Graph

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