derivative of ln(\sqrt[4]{(x-1/(x+1)}))

Lösung

\frac{d}{d x} (ln (4 \frac{x - 1}{x + 1}))

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

Schritte zur Lösung

\frac{d}{d x} (ln (4 \frac{x - 1}{x + 1}))

Wende die Kettenregel an:

\frac{1}{4 \frac{x - 1}{x + 1}} \frac{d}{d x} (4 \frac{x - 1}{x + 1})

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

\frac{d}{d x} (4 \frac{x - 1}{x + 1}) = \frac{1}{2 ( x - 1 ) ^{\frac{3}{4}} ( x + 1 ) ^{\frac{5}{4}}}

= \frac{1}{4 \frac{x - 1}{x + 1}} \cdot \frac{1}{2 ( x - 1 ) ^{\frac{3}{4}} ( x + 1 ) ^{\frac{5}{4}}}

Vereinfache

\frac{1}{4 \frac{x - 1}{x + 1}} \cdot \frac{1}{2 ( x - 1 ) ^{\frac{3}{4}} ( x + 1 ) ^{\frac{5}{4}}} : \frac{1}{2 ( x + 1 ) 4 x - 1 ( x - 1 ) ^{\frac{3}{4}}}

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

d er i v a t i v e f (x) = \frac{1}{5} x^{2} + \frac{200000}{x}

(1 + x^{2}) y^{^{''}} + y^{^{'}} x + a x = 0

f (t) = 3 cos (t)

\int \frac{sec ( x )}{2 sec ( x ) + 1} d x

t an g e n t x^{2} + y^{2} = 100, (- 6, 8)