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}}

\frac{d}{d x} ((1 - 3 x^{2})^{\frac{1}{s i n ^{2} ( x )}})

\int [x (x - 1)] d x

x \to 1 + lim (\frac{4}{x ^{3} - 1})

\int 3 x^{2} (x^{3} + 4)^{4} d x

f (x) = ln (sin (2 x))