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

Lösung

ableitung von

\frac{x + 1}{x ^{2}}

\frac{- x - 2}{x ^{3}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{1 \cdot x ^{2} - 2 x ( x + 1 )}{( x ^{2} ) ^{2}} : \frac{- x - 2}{x ^{3}}

= \frac{- x - 2}{x ^{3}}

x \to 2 lim (lo g_{4} (x - 2))

\frac{d y}{d x} + 3 x^{2} y = x^{2}

\frac{d y}{d x} = 10 x e^{5 y}

d er i v a t i v e f (x) = \frac{2}{x}

\frac{d}{d x} (sin^{3} (4 x^{2} - 1))