derivative f(x)=(x^2-2sqrt(x))/x

Lösung

ableitung von

f (x) = \frac{x ^{2} - 2 x}{x}

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

Schritte zur Lösung

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

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

\frac{d x}{d x} = 1

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

Vereinfache

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

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

d er i v a t i v e (x^{2} - 2 x)^{3}

d er i v a t i v e in (x^{2})

\int_{0}^{c} 10 e^{2 x} d x

\int (\frac{3}{x ^{3}}) d x

\frac{d}{d t} (e^{i t})