derivative of (1-2x/(3x^2))

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{3} \frac{d}{d x} (\frac{1 - 2 x}{x ^{2}})

Wende die Quotientenregel an:

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

= \frac{1}{3} \cdot \frac{\frac{d}{d x} ( 1 - 2 x ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( 1 - 2 x )}{( x ^{2} ) ^{2}}

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

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

= \frac{1}{3} \cdot \frac{( - 2 ) x ^{2} - 2 x ( 1 - 2 x )}{( x ^{2} ) ^{2}}

Vereinfache

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

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

\frac{d}{d x} ((\frac{x + 5}{x ^{2} + 2})^{2})

\frac{d ^{2}}{d x ^{2}} (e^{\frac{6}{x}})

x \to \infty lim (- 3 x^{3} + x)

a re a y = 0, y = 3 (x^{3} - x)

x \to 0 lim (cos (x))