(\partial)/(\partial x)(ln((2xy)/(7z)))

Lösung

\frac{\partial}{\partial x} (ln (\frac{2 x y}{7 z}))

\frac{1}{x}

Schritte zur Lösung

\frac{\partial}{\partial x} (ln (\frac{2 x y}{7 z}))

Behandle

y, z

als Konstanten

Wende die Kettenregel an:

\frac{1}{\frac{2 x y}{7 z}} \frac{\partial}{\partial x} (\frac{2 x y}{7 z})

= \frac{1}{\frac{2 x y}{7 z}} \frac{\partial}{\partial x} (\frac{2 x y}{7 z})

\frac{\partial}{\partial x} (\frac{2 x y}{7 z}) = \frac{2 y}{7 z}

= \frac{1}{\frac{2 x y}{7 z}} \cdot \frac{2 y}{7 z}

Vereinfache

\frac{1}{\frac{2 x y}{7 z}} \cdot \frac{2 y}{7 z} : \frac{1}{x}

= \frac{1}{x}

t an g e n t f (x) = 1 3 x, at x = 1

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