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

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\frac{\partial}{\partial x} (x y + \frac{1}{x} + \frac{1}{y})

t an g e n t f (x) = 9 - 6 x, at x = - 1

in v erse l a pl a ce - \frac{3}{s + 3} + \frac{4}{s - 4}

\int \frac{8}{x ^{- 1} + 2} d x

s l o p e y = 4 x^{2} - x