derivative of sqrt((ln(x+1)/(ln(x)-1)))

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

\frac{1}{2 \frac{l n ( x ) + 1}{l n ( x ) - 1}} \frac{d}{d x} (\frac{ln ( x ) + 1}{ln ( x ) - 1})

= \frac{1}{2 \frac{l n ( x ) + 1}{l n ( x ) - 1}} \frac{d}{d x} (\frac{ln ( x ) + 1}{ln ( x ) - 1})

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

= \frac{1}{2 \frac{l n ( x ) + 1}{l n ( x ) - 1}} (- \frac{2}{x ( ln ( x ) - 1 ) ^{2}})

Vereinfache

\frac{1}{2 \frac{l n ( x ) + 1}{l n ( x ) - 1}} (- \frac{2}{x ( ln ( x ) - 1 ) ^{2}}) : - \frac{1}{x ln ( x ) + 1 ( ln ( x ) - 1 ) ^{\frac{3}{2}}}

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

x \to - 2 lim (\frac{2 - ∣ x ∣}{2 + x})

y^{^{'}} = 2 x y + x y^{2}

l a pl a ce t r an s f or m 2 cos (t) - 2

\frac{d}{d x} (\frac{( 6 x ^{2} + 8 x + 8 )}{x})

\int_{11}^{12.5} 3 e^{- 3 x} d x