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Beliebt Rechnen >

(\partial)/(\partial y)(-1/4 (y^2+x^2))

Lösung

\frac{\partial}{\partial y} (- \frac{1}{4} (y^{2} + x^{2}))

Lösung

- \frac{y}{2}

Schritte zur Lösung

\frac{\partial}{\partial y} (- \frac{1}{4} (y^{2} + x^{2}))

Behandle

x

als Konstante

Entferne die Konstante:

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

= - \frac{1}{4} \frac{\partial}{\partial y} (y^{2} + x^{2})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= - \frac{1}{4} (\frac{\partial}{\partial y} (y^{2}) + \frac{\partial}{\partial y} (x^{2}))

\frac{\partial}{\partial y} (y^{2}) = 2 y

\frac{\partial}{\partial y} (x^{2}) = 0

= - \frac{1}{4} (2 y + 0)

Vereinfache

- \frac{1}{4} (2 y + 0) : - \frac{y}{2}

= - \frac{y}{2}

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