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

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

in v erse l a pl a ce \frac{8}{s - 1} - \frac{3}{s}

x \to 0 lim (\frac{x}{x ^{2} + 4 x})

n = 1 \sum \infty (- 3)^{n} x^{n}

x \to 4 - lim (\frac{∣ 2 x ∣}{x})

d er i v a t i v e - 32 t