derivative of ((x^2-4x)/(x+1))

Lösung

\frac{d}{d x} (\frac{( x ^{2} - 4 x )}{x + 1})

\frac{x ^{2} + 2 x - 4}{( x + 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{( x ^{2} - 4 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} - 4 x ) ( x + 1 ) - \frac{d}{d x} ( x + 1 ) ( x ^{2} - 4 x )}{( x + 1 ) ^{2}}

\frac{d}{d x} (x^{2} - 4 x) = 2 x - 4

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

= \frac{( 2 x - 4 ) ( x + 1 ) - 1 \cdot ( x ^{2} - 4 x )}{( x + 1 ) ^{2}}

Vereinfache

\frac{( 2 x - 4 ) ( x + 1 ) - 1 \cdot ( x ^{2} - 4 x )}{( x + 1 ) ^{2}} : \frac{x ^{2} + 2 x - 4}{( x + 1 ) ^{2}}

= \frac{x ^{2} + 2 x - 4}{( x + 1 ) ^{2}}

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

\frac{\partial}{\partial x} (sin (y^{2}) + 6 e^{x})

d er i v a t i v e e^{2 y}

in v erse l a pl a ce (\frac{( s + 1 )}{s ^{4}})^{3}

\int x (x + 1)^{5} d x