derivative f(x)=(\sqrt[3]{x})/(x-6)

Lösung

ableitung von

f (x) = \frac{3 x}{x - 6}

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

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x}{x - 6})

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (x - 6) = 1

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

Vereinfache

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

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

x \to 3 lim (f (x) (x - 1))

\frac{\partial}{\partial y} (x - y)

x \to 0 lim (\frac{( 1 1 ^{x} - 1 )}{x})

\int \frac{5}{cos ( x ) - 1} d x

\int y cos (\frac{x}{y}) d x