(\partial)/(\partial x)(ln((2xy)/(5z)))

Lösung

\frac{\partial}{\partial x} (ln (\frac{2 x y}{5 z}))

\frac{1}{x}

Schritte zur Lösung

\frac{\partial}{\partial x} (ln (\frac{2 x y}{5 z}))

Behandle

y, z

als Konstanten

Wende die Kettenregel an:

\frac{1}{\frac{2 x y}{5 z}} \frac{\partial}{\partial x} (\frac{2 x y}{5 z})

= \frac{1}{\frac{2 x y}{5 z}} \frac{\partial}{\partial x} (\frac{2 x y}{5 z})

\frac{\partial}{\partial x} (\frac{2 x y}{5 z}) = \frac{2 y}{5 z}

= \frac{1}{\frac{2 x y}{5 z}} \cdot \frac{2 y}{5 z}

Vereinfache

\frac{1}{\frac{2 x y}{5 z}} \cdot \frac{2 y}{5 z} : \frac{1}{x}

= \frac{1}{x}

\int - \frac{9}{x ^{10}} d x

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x \to - 2 lim (\frac{1}{2 x})

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