derivative of (3x^2-12/(8x))

Lösung

\frac{d}{d x} (\frac{3 x ^{2} - 12}{8 x})

\frac{3 x ^{2} + 12}{8 x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x ^{2} - 12}{8 x})

Entferne die Konstante:

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

= \frac{1}{8} \frac{d}{d x} (\frac{3 x ^{2} - 12}{x})

Wende die Quotientenregel an:

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

= \frac{1}{8} \cdot \frac{\frac{d}{d x} ( 3 x ^{2} - 12 ) x - \frac{d x}{d x} ( 3 x ^{2} - 12 )}{x ^{2}}

\frac{d}{d x} (3 x^{2} - 12) = 6 x

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

= \frac{1}{8} \cdot \frac{6 xx - 1 \cdot ( 3 x ^{2} - 12 )}{x ^{2}}

Vereinfache

\frac{1}{8} \cdot \frac{6 xx - 1 \cdot ( 3 x ^{2} - 12 )}{x ^{2}} : \frac{3 x ^{2} + 12}{8 x ^{2}}

= \frac{3 x ^{2} + 12}{8 x ^{2}}

\int + ln (3) e^{x} d x

\int 3 x - 1 d x

\int s e^{- s x y} d x

d er i v a t i v e \frac{5 - x e ^{x}}{x + e ^{x}}

z \to 1 lim (A r g (z))