(\partial)/(\partial x)(30-(x^2+y^2))

Lösung

\frac{\partial}{\partial x} (30 - (x^{2} + y^{2}))

- 2 x

Schritte zur Lösung

\frac{\partial}{\partial x} (30 - (x^{2} + y^{2}))

Vereinfache

30 - (x^{2} + y^{2}) : 30 - x^{2} - y^{2}

= \frac{\partial}{\partial x} (30 - x^{2} - y^{2})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (30) - \frac{\partial}{\partial x} (x^{2}) - \frac{\partial}{\partial x} (y^{2})

\frac{\partial}{\partial x} (30) = 0

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

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

= 0 - 2 x - 0

Vereinfache

= - 2 x

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