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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

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

f (t) = 2 cos (t)

a re a x = - 2, x = 1, y = 3 x, y = x^{2} - 4

y^{^{''}} + y = 5 csc^{2} (t)

d er i v a t i v e f (x) = 8 x^{10} + 6 x^{6}