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

Lösung

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

\frac{2}{3 x ^{\frac{1}{3}}}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

= \frac{2}{3 x ^{\frac{1}{3}}} + 0

Vereinfache

= \frac{2}{3 x ^{\frac{1}{3}}}

\int \frac{1}{64 + x ^{2}} d x

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t a y l or \frac{1}{1 + x ^{2}}, 0

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