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Beliebt Rechnen >

(\partial)/(\partial x)((e^y)/(x+y^2))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

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

Wende die Kettenregel an:

- \frac{1}{( x + y ^{2} ) ^{2}} \frac{\partial}{\partial x} (x + y^{2})

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

\frac{\partial}{\partial x} (x + y^{2}) = 1

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

Vereinfache

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

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

Beliebte Beispiele

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d er i v a t i v e f (x) = 2 x^{2} - 3 x + 4

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\int \frac{7}{( x ^{2} + 3 x - 10 )} d x

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\int sin^{5} (d) x d x

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d er i v a t i v e tan (θ)