derivative ln((x^2)/(2x^2+3x+2))

Lösung

ableitung von

ln (\frac{x ^{2}}{2 x ^{2} + 3 x + 2})

\frac{3 x + 4}{x ( 2 x ^{2} + 3 x + 2 )}

Schritte zur Lösung

\frac{d}{d x} (ln (\frac{x ^{2}}{2 x ^{2} + 3 x + 2}))

Wende die Kettenregel an:

\frac{1}{\frac{x ^{2}}{2 x ^{2} + 3 x + 2}} \frac{d}{d x} (\frac{x ^{2}}{2 x ^{2} + 3 x + 2})

= \frac{1}{\frac{x ^{2}}{2 x ^{2} + 3 x + 2}} \frac{d}{d x} (\frac{x ^{2}}{2 x ^{2} + 3 x + 2})

\frac{d}{d x} (\frac{x ^{2}}{2 x ^{2} + 3 x + 2}) = \frac{3 x ^{2} + 4 x}{( 2 x ^{2} + 3 x + 2 ) ^{2}}

= \frac{1}{\frac{x ^{2}}{2 x ^{2} + 3 x + 2}} \cdot \frac{3 x ^{2} + 4 x}{( 2 x ^{2} + 3 x + 2 ) ^{2}}

Vereinfache

\frac{1}{\frac{x ^{2}}{2 x ^{2} + 3 x + 2}} \cdot \frac{3 x ^{2} + 4 x}{( 2 x ^{2} + 3 x + 2 ) ^{2}} : \frac{3 x + 4}{x ( 2 x ^{2} + 3 x + 2 )}

= \frac{3 x + 4}{x ( 2 x ^{2} + 3 x + 2 )}

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