derivative f(x)=(3x+2)/(3x-2)

Lösung

ableitung von

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

- \frac{12}{( 3 x - 2 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{3 ( 3 x - 2 ) - 3 ( 3 x + 2 )}{( 3 x - 2 ) ^{2}} : - \frac{12}{( 3 x - 2 ) ^{2}}

= - \frac{12}{( 3 x - 2 ) ^{2}}

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

\frac{d}{d x} (25 + x^{2})

s l o p e (2, - 2), (9, 3)

d er i v a t i v e 4 arcsin (x^{2})

\frac{d}{d x} (A t e^{- t})