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}}

\int (3 x^{4} + x^{2} + 2) d x

\frac{\partial}{\partial x} (12 x^{2} y^{5} + x^{2} y^{2})

x \to 0 lim (x^{4} f (x))

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

2 y (x + 1) d y = x d x