(\partial)/(\partial x)(10-(3x^2+3y^2))

Lösung

\frac{\partial}{\partial x} (10 - (3 x^{2} + 3 y^{2}))

- 6 x

Schritte zur Lösung

\frac{\partial}{\partial x} (10 - (3 x^{2} + 3 y^{2}))

Vereinfache

10 - (3 x^{2} + 3 y^{2}) : 10 - 3 x^{2} - 3 y^{2}

= \frac{\partial}{\partial x} (10 - 3 x^{2} - 3 y^{2})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (10) - \frac{\partial}{\partial x} (3 x^{2}) - \frac{\partial}{\partial x} (3 y^{2})

\frac{\partial}{\partial x} (10) = 0

\frac{\partial}{\partial x} (3 x^{2}) = 6 x

\frac{\partial}{\partial x} (3 y^{2}) = 0

= 0 - 6 x - 0

Vereinfache

= - 6 x

\frac{d}{d x} (3 x^{2} - 4 x + 1)

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