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

Lösung

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

\frac{- 3 x ^{2} - 6 x + 9}{( x ^{2} - 3 x ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Multipliziere aus

2 x (x^{2} - 3 x) - (2 x - 3) (x^{2} + 3) : - 3 x^{2} - 6 x + 9

= \frac{- 3 x ^{2} - 6 x + 9}{( x ^{2} - 3 x ) ^{2}}

\int 4 r^{2} + 1 r d r

\frac{d}{d x} (arccos (\frac{x}{8}))

\frac{d}{d x} (π^{x})

\int \frac{1}{x 9 x ^{2} - 25} d x

\frac{d y}{d x} = \frac{4}{x ^{2} e ^{2 y}}