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Beliebt Rechnen >

derivative of (e^x/x)

Lösung

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

Lösung

\frac{e ^{x} x - e ^{x}}{x ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( e ^{x} ) x - \frac{d x}{d x} e ^{x}}{x ^{2}}

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

\frac{d x}{d x} = 1

= \frac{e ^{x} x - 1 \cdot e ^{x}}{x ^{2}}

Vereinfache

= \frac{e ^{x} x - e ^{x}}{x ^{2}}

Graph

Beliebte Beispiele

limit as x approaches 0+of arcsin(2x-1)

x \to 0 + lim (arcsin (2 x - 1))

implicit (dy)/(dx),3x^3y=6

im pl i c i t \frac{d y}{d x}, 3 x^{3} y = 6

derivative f(x)=-1/4 x^4+27/2 x^2

d er i v a t i v e f (x) = - \frac{1}{4} x^{4} + \frac{27}{2} x^{2}

integral of (m^2)/(m+1)

\int \frac{m ^{2}}{m + 1} d m

derivative of (x+10/(x-10))

\frac{d}{d x} (\frac{x + 10}{x - 10})