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

Lösung

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

- \frac{2}{x}

Schritte zur Lösung

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

Vereinfache

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

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= - \frac{2}{x}