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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

d er i v a t i v e \frac{5}{x + 1}

\frac{d}{d x} (sec (x))

\int_{1}^{2} 11 e^{\frac{1}{x}} d x

\int 4 cos (θ) sin (θ) d θ

x \to 0 + lim (\frac{e ^{x} - 1}{x})