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

Lösung

\frac{d}{d x} (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 )}

t an g e n t y = \frac{π}{( 2 x ) ^{4}}

\int \frac{2}{x ^{2} + 9} d x

\frac{x d y}{d x} = 2 y

im pl i c i t \frac{d y}{d x}, y = 2 9^{x}

t an g e n t f (x) = 2 x^{3} + 3 x^{2} - 12 x + 2