(\partial)/(\partial x)((y/x)^{1/z})

Lösung

\frac{\partial}{\partial x} ((\frac{y}{x})^{\frac{1}{z}})

- \frac{y ^{\frac{1}{z}}}{z x ^{\frac{1 + z}{z}}}

Schritte zur Lösung

\frac{\partial}{\partial x} ((\frac{y}{x})^{\frac{1}{z}})

Behandle

y, z

als Konstanten

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{( \frac{y}{x} ) ^{\frac{1 - z}{z}}}{z} (- \frac{y}{x ^{2}}) : - \frac{y ^{\frac{1}{z}}}{z x ^{\frac{1 + z}{z}}}

= - \frac{y ^{\frac{1}{z}}}{z x ^{\frac{1 + z}{z}}}

\frac{d}{d x} (r (x) (x)^{2} - x^{2})

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\int \frac{4}{b ^{4} x ^{2} + m ^{2}} d x