derivative of (2x+3/(3x-2))

Lösung

\frac{d}{d x} (\frac{2 x + 3}{3 x - 2})

- \frac{13}{( 3 x - 2 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x + 3}{3 x - 2})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d}{d x} (3 x - 2) = 3

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

Vereinfache

\frac{2 ( 3 x - 2 ) - 3 ( 2 x + 3 )}{( 3 x - 2 ) ^{2}} : - \frac{13}{( 3 x - 2 ) ^{2}}

= - \frac{13}{( 3 x - 2 ) ^{2}}

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

t a y l or x, 100

\frac{d y}{d x} = x + 2 y, y (0) = 7

\frac{d}{d x} (e^{x} \cdot cos (y))

\int y e^{y} d y