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Beliebt Rechnen >

derivative y=ln((5x)/(7+x))

Lösung

ableitung von

y = ln (\frac{5 x}{7 + x})

Lösung

\frac{7}{x ( x + 7 )}

Schritte zur Lösung

\frac{d}{d x} (ln (\frac{5 x}{7 + x}))

Wende die Kettenregel an:

\frac{1}{\frac{5 x}{7 + x}} \frac{d}{d x} (\frac{5 x}{7 + x})

= \frac{1}{\frac{5 x}{7 + x}} \frac{d}{d x} (\frac{5 x}{7 + x})

\frac{d}{d x} (\frac{5 x}{7 + x}) = \frac{35}{( 7 + x ) ^{2}}

= \frac{1}{\frac{5 x}{7 + x}} \cdot \frac{35}{( 7 + x ) ^{2}}

Vereinfache

\frac{1}{\frac{5 x}{7 + x}} \cdot \frac{35}{( 7 + x ) ^{2}} : \frac{7}{x ( x + 7 )}

= \frac{7}{x ( x + 7 )}

Graph

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