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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

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

Vereinfache

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

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

s l o p e \frac{1}{x - 4}

x \to 1 + lim (\frac{2}{x} - \frac{1}{ln ( x )})

\frac{\partial}{\partial x} (2 y \cdot arctan (\frac{x}{y}))

d er i v a t i v e 6 x + 4

x \to 6 lim (- 5 x^{2} + 6 x + 8)