derivative of ln(\sqrt[3]{(x-1/(x+1)}))

Lösung

\frac{d}{d x} (ln (3 \frac{x - 1}{x + 1}))

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

Schritte zur Lösung

\frac{d}{d x} (ln (3 \frac{x - 1}{x + 1}))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

d er i v a t i v e 3 x + 1

x \to 2 lim (x^{2} + 8)

t a y l or x^{7} e^{x} 5

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

2 y^{^{'}} + 3 y = 5