derivative of ln(\sqrt[6]{(x-5/(x+5)}))

Lösung

\frac{d}{d x} (ln (6 \frac{x - 5}{x + 5}))

\frac{5}{3 ( x + 5 ) 6 x - 5 ( x - 5 ) ^{\frac{5}{6}}}

Schritte zur Lösung

\frac{d}{d x} (ln (6 \frac{x - 5}{x + 5}))

Wende die Kettenregel an:

\frac{1}{6 \frac{x - 5}{x + 5}} \frac{d}{d x} (6 \frac{x - 5}{x + 5})

= \frac{1}{6 \frac{x - 5}{x + 5}} \frac{d}{d x} (6 \frac{x - 5}{x + 5})

\frac{d}{d x} (6 \frac{x - 5}{x + 5}) = \frac{5}{3 ( x - 5 ) ^{\frac{5}{6}} ( x + 5 ) ^{\frac{7}{6}}}

= \frac{1}{6 \frac{x - 5}{x + 5}} \cdot \frac{5}{3 ( x - 5 ) ^{\frac{5}{6}} ( x + 5 ) ^{\frac{7}{6}}}

Vereinfache

\frac{1}{6 \frac{x - 5}{x + 5}} \cdot \frac{5}{3 ( x - 5 ) ^{\frac{5}{6}} ( x + 5 ) ^{\frac{7}{6}}} : \frac{5}{3 ( x + 5 ) 6 x - 5 ( x - 5 ) ^{\frac{5}{6}}}

= \frac{5}{3 ( x + 5 ) 6 x - 5 ( x - 5 ) ^{\frac{5}{6}}}

in v erse l a pl a ce \frac{2 s e ^{- 2 s}}{5 s ^{2} + 45}

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

y^{^{''}} - y^{^{'}} - 2 y = 4 e^{- t}

d er i v a t i v e f (x) = \frac{2}{x - 7}

\int 8 x e^{- x^{2}} d x