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Beliebt Rechnen >

d/(dy)(e^{x/y})

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

e^{\frac{x}{y}} (- \frac{x}{y ^{2}}) : - \frac{e ^{\frac{x}{y}} x}{y ^{2}}

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

Beliebte Beispiele

limit as x approaches 6 of-1/(x-6)

x \to 6 lim (- \frac{1}{x - 6})

(dy}{dx}=\frac{x^2+2y)/x

\frac{d y}{d x} = \frac{x ^{2} + 2 y}{x}

integral of ((x+11)/(x-9))

\int (\frac{x + 11}{x - 9}) d x

integral from 0 to 3 of f(x)

\int_{0}^{3} f (x) d x

integral of x^3e^{-x^4}

\int x^{3} e^{- x^{4}} d x