derivative of (x^2-2/x)

Lösung

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

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

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

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

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

Vereinfache

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

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

t an g e n t x^{2} + 2 x y - y^{2} + x = 5, (3, 7)

\frac{d}{d t} (t ln (t))

x \to 0 + lim (\frac{x}{ln ( x )})

a re a f (x) = x^{2} + 4 x - 5, - 3, 3

x \to 3 lim (\frac{5 x}{x - 3})