(\partial)/(\partial y)(ln((y/x)^2))

Lösung

\frac{\partial}{\partial y} (ln ((\frac{y}{x})^{2}))

\frac{2}{y}

Schritte zur Lösung

\frac{\partial}{\partial y} (ln ((\frac{y}{x})^{2}))

Vereinfache

ln ((\frac{y}{x})^{2}) : ln (\frac{y ^{2}}{x ^{2}})

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

Behandle

x

als Konstante

Wende die Kettenregel an:

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

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

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

= \frac{1}{\frac{y ^{2}}{x ^{2}}} \cdot \frac{2 y}{x ^{2}}

Vereinfache

\frac{1}{\frac{y ^{2}}{x ^{2}}} \cdot \frac{2 y}{x ^{2}} : \frac{2}{y}

= \frac{2}{y}

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