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Beliebt Rechnen >

derivative of e^{\sqrt[5]{x}}

Lösung

\frac{d}{d x} (e^{5 x})

Lösung

\frac{e ^{5 x}}{5 x ^{\frac{4}{5}}}

Schritte zur Lösung

\frac{d}{d x} (e^{5 x})

Wende die Kettenregel an:

e^{5 x} \frac{d}{d x} (5 x)

= e^{5 x} \frac{d}{d x} (5 x)

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

= e^{5 x} \frac{1}{5 x ^{\frac{4}{5}}}

Vereinfache

e^{5 x} \frac{1}{5 x ^{\frac{4}{5}}} : \frac{e ^{5 x}}{5 x ^{\frac{4}{5}}}

= \frac{e ^{5 x}}{5 x ^{\frac{4}{5}}}

Graph

Beliebte Beispiele

integral of (13sqrt(x)+sqrt(3))

\int (13 x + 3) d x

d er i v a t i v e x^{a}

d/(dt)(tan(sqrt(5t)))

\frac{d}{d t} (tan (5 t))

tangent y=-6x^2+4

t an g e n t y = - 6 x^{2} + 4

limit as x approaches 0+of ln(x)sqrt(x)

x \to 0 + lim (ln (x) x)