derivative of (3x-2/(2x+1))

Lösung

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

\frac{7}{( 2 x + 1 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Multipliziere aus

3 (2 x + 1) - 2 (3 x - 2) : 7

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

x \to 3 - lim (\frac{2 - x}{x - 3})

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

\int \frac{7}{( 7 ^{2} + x ^{2} ) ^{\frac{3}{2}}} d x

x \to 0 lim (x [\frac{1}{x}])

\frac{d}{d s} (\frac{1}{s})