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

Lösung

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

x^{p - 1} (x^{p} + y^{p})^{\frac{1 - p}{p}}

Schritte zur Lösung

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

Behandle

p, y

als Konstante

Wende die Kettenregel an:

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

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

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

= \frac{( x ^{p} + y ^{p} ) ^{\frac{1 - p}{p}}}{p} p x^{p - 1}

Vereinfache

\frac{( x ^{p} + y ^{p} ) ^{\frac{1 - p}{p}}}{p} p x^{p - 1} : x^{p - 1} (x^{p} + y^{p})^{\frac{1 - p}{p}}

= x^{p - 1} (x^{p} + y^{p})^{\frac{1 - p}{p}}

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