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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

\frac{1}{3 \frac{3 x}{x + 2}} \frac{d}{d x} (3 \frac{3 x}{x + 2})

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

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

= \frac{1}{3 \frac{3 x}{x + 2}} \cdot \frac{2}{3 ^{\frac{2}{3}} x ^{\frac{2}{3}} ( x + 2 ) ^{\frac{4}{3}}}

Vereinfache

\frac{1}{3 \frac{3 x}{x + 2}} \cdot \frac{2}{3 ^{\frac{2}{3}} x ^{\frac{2}{3}} ( x + 2 ) ^{\frac{4}{3}}} : \frac{2}{3 3 \cdot 3 ^{\frac{2}{3}} 3 x x ^{\frac{2}{3}} ( x + 2 )}

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

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

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

x \to 0 lim (\frac{5}{x ^{2} - x})

\frac{d}{d x} (\frac{32 x}{( x ^{2} + 3 ) ^{2}})

d er i v a t i v e 4 t^{- \frac{3}{8}}