derivative of (sqrt(x)/(\sqrt[3]{2x)})

Lösung

\frac{d}{d x} (\frac{x}{3 2 x})

\frac{1}{6 3 2 6 x x ^{\frac{2}{3}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{3 2 x})

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{\frac{1}{2 x} 3 2 x - \frac{2 ^{\frac{1}{3}}}{3 x ^{\frac{2}{3}}} x}{( 3 2 x ) ^{2}} : \frac{1}{6 3 2 6 x x ^{\frac{2}{3}}}

= \frac{1}{6 3 2 6 x x ^{\frac{2}{3}}}

\frac{\partial}{\partial y} (8 x^{5 y})

\frac{d y}{d t} = 2 y (1 - \frac{y}{2})

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

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

d er i v a t i v e f (x) = (x + 1)^{3}