derivative (3x-5)/(x^2-1)

Lösung

ableitung von

\frac{3 x - 5}{x ^{2} - 1}

\frac{- 3 x ^{2} + 10 x - 3}{( x ^{2} - 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x - 5}{x ^{2} - 1})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 3 x - 5 ) ( x ^{2} - 1 ) - \frac{d}{d x} ( x ^{2} - 1 ) ( 3 x - 5 )}{( x ^{2} - 1 ) ^{2}}

\frac{d}{d x} (3 x - 5) = 3

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

= \frac{3 ( x ^{2} - 1 ) - 2 x ( 3 x - 5 )}{( x ^{2} - 1 ) ^{2}}

Multipliziere aus

3 (x^{2} - 1) - 2 x (3 x - 5) : - 3 x^{2} + 10 x - 3

= \frac{- 3 x ^{2} + 10 x - 3}{( x ^{2} - 1 ) ^{2}}

x \to - 2 lim ((x^{3}) (5 - 3 x^{2}))

\frac{d}{d x} (sin (3 x) + cos (6 x))

\int e^{i wt} d t

\frac{d}{d x} (1 - (\frac{x + b + c}{( 3 a )}))

\int_{3}^{5} \frac{1}{x + 1} d x