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

Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{3 ( x ^{2} + y ^{2} ) ^{\frac{2}{3}}} \cdot 2 x : \frac{2 x}{3 ( x ^{2} + y ^{2} ) ^{\frac{2}{3}}}

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

x \to 1 lim (\frac{- 1}{x - 1})

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