(\partial)/(\partial x)(3-(x^2+y^2)^{1/3})

Lösung

\frac{\partial}{\partial x} (3 - (x^{2} + y^{2})^{\frac{1}{3}})

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

Schritte zur Lösung

\frac{\partial}{\partial x} (3 - (x^{2} + y^{2})^{\frac{1}{3}})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (3) - \frac{\partial}{\partial x} ((x^{2} + y^{2})^{\frac{1}{3}})

\frac{\partial}{\partial x} (3) = 0

\frac{\partial}{\partial x} ((x^{2} + y^{2})^{\frac{1}{3}}) = \frac{2 x}{3 ( x ^{2} + y ^{2} ) ^{\frac{2}{3}}}

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

Vereinfache

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

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