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Beliebt Rechnen >

derivative-y/(x+e^y)

Lösung

ableitung von

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

Lösung

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Quotientenregel an:

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

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

\frac{d y}{d y} = 1

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

= - \frac{1 \cdot ( x + e ^{y} ) - e ^{y} y}{( x + e ^{y} ) ^{2}}

Vereinfache

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

Beliebte Beispiele

integral from 0 to 3 of (6t)/((t-4)^2)

\int_{0}^{3} \frac{6 t}{( t - 4 ) ^{2}} d t

integral of (2xe^x)/((x+1)^2)

\int \frac{2 x e ^{x}}{( x + 1 ) ^{2}} d x

(\partial)/(\partial x)(y-x^2ye^{-y})

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

taylor sin(x^2),0

t a y l or sin (x^{2}), 0

y^{''}+y^'-2y=sin(x)

y^{^{''}} + y^{^{'}} - 2 y = sin (x)