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

Lösung

ableitung von

\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}}

\int_{1}^{13} 4 x^{- 2} d x

\int \frac{1}{x 49 x ^{2} + 1} d x

\int sec^{7} (5 x + 4) d x

d er i v a t i v e \frac{x}{1 + x ^{2}}

x \to 4 + lim (\frac{7}{( x - 4 ) ^{2}})