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Beliebt Rechnen >

(\partial)/(\partial x)((x-1)^{2/3}(y^2-4))

Lösung

\frac{\partial}{\partial x} ((x - 1)^{\frac{2}{3}} (y^{2} - 4))

Lösung

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

Schritte zur Lösung

\frac{\partial}{\partial x} ((x - 1)^{\frac{2}{3}} (y^{2} - 4))

Behandle

y

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= (y^{2} - 4) \frac{\partial}{\partial x} ((x - 1)^{\frac{2}{3}})

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial x} (x - 1) = 1

= (y^{2} - 4) \frac{2}{3 ( x - 1 ) ^{\frac{1}{3}}} \cdot 1

Vereinfache

(y^{2} - 4) \frac{2}{3 ( x - 1 ) ^{\frac{1}{3}}} \cdot 1 : \frac{2 ( y ^{2} - 4 )}{3 ( x - 1 ) ^{\frac{1}{3}}}

= \frac{2 ( y ^{2} - 4 )}{3 ( x - 1 ) ^{\frac{1}{3}}}

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