(\partial)/(\partial y)(ln((y^9)/(x^7)))

Lösung

\frac{\partial}{\partial y} (ln (\frac{y ^{9}}{x ^{7}}))

\frac{9}{y}

Schritte zur Lösung

\frac{\partial}{\partial y} (ln (\frac{y ^{9}}{x ^{7}}))

Behandle

x

als Konstante

Wende die Kettenregel an:

\frac{1}{\frac{y ^{9}}{x ^{7}}} \frac{\partial}{\partial y} (\frac{y ^{9}}{x ^{7}})

= \frac{1}{\frac{y ^{9}}{x ^{7}}} \frac{\partial}{\partial y} (\frac{y ^{9}}{x ^{7}})

\frac{\partial}{\partial y} (\frac{y ^{9}}{x ^{7}}) = \frac{9 y ^{8}}{x ^{7}}

= \frac{1}{\frac{y ^{9}}{x ^{7}}} \cdot \frac{9 y ^{8}}{x ^{7}}

Vereinfache

\frac{1}{\frac{y ^{9}}{x ^{7}}} \cdot \frac{9 y ^{8}}{x ^{7}} : \frac{9}{y}

= \frac{9}{y}

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