derivative of (x^2-2x/(x^2+5x))

Lösung

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

\frac{7}{( x + 5 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (x^{2} + 5 x) = 2 x + 5

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

Vereinfache

\frac{( 2 x - 2 ) ( x ^{2} + 5 x ) - ( 2 x + 5 ) ( x ^{2} - 2 x )}{( x ^{2} + 5 x ) ^{2}} : \frac{7}{( x + 5 ) ^{2}}

= \frac{7}{( x + 5 ) ^{2}}

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

x^{2} \frac{d y}{d x} - y x = 0

n = 0 \sum \infty e^{- 2 n}

x \to - 4 - lim (5 x + 20 - 8)

(e^{y} + 1)^{2} e^{- y} d x + (e^{x} + 1)^{3} e^{- x} d y = 0