derivative of ((x^2-6x)/(x+1))

Lösung

\frac{d}{d x} (\frac{( x ^{2} - 6 x )}{x + 1})

\frac{x ^{2} + 2 x - 6}{( x + 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{( x ^{2} - 6 x )}{x + 1})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} - 6 x ) ( x + 1 ) - \frac{d}{d x} ( x + 1 ) ( x ^{2} - 6 x )}{( x + 1 ) ^{2}}

\frac{d}{d x} (x^{2} - 6 x) = 2 x - 6

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

= \frac{( 2 x - 6 ) ( x + 1 ) - 1 \cdot ( x ^{2} - 6 x )}{( x + 1 ) ^{2}}

Vereinfache

\frac{( 2 x - 6 ) ( x + 1 ) - 1 \cdot ( x ^{2} - 6 x )}{( x + 1 ) ^{2}} : \frac{x ^{2} + 2 x - 6}{( x + 1 ) ^{2}}

= \frac{x ^{2} + 2 x - 6}{( x + 1 ) ^{2}}

a re a y = \frac{2}{x}, y = 8 x, y = \frac{1}{8} x

\int_{2}^{\infty} \frac{1}{ln ( x )} d x

x \to \infty lim (- \frac{1}{2} e^{- x^{2}})

\frac{d}{d x} (e^{2 x} cos (x))

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