derivative of ln((5x+1/(5x-1)))

Lösung

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

- \frac{10}{( 5 x + 1 ) ( 5 x - 1 )}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (\frac{5 x + 1}{5 x - 1}) = - \frac{10}{( 5 x - 1 ) ^{2}}

= \frac{1}{\frac{5 x + 1}{5 x - 1}} (- \frac{10}{( 5 x - 1 ) ^{2}})

Vereinfache

\frac{1}{\frac{5 x + 1}{5 x - 1}} (- \frac{10}{( 5 x - 1 ) ^{2}}) : - \frac{10}{( 5 x + 1 ) ( 5 x - 1 )}

= - \frac{10}{( 5 x + 1 ) ( 5 x - 1 )}

n = 1 \sum \infty n^{2} + 1

im pl i c i t 2 x y - y^{2} = - 1

\int (3 x^{2} + 4 x - 6) d x

\frac{d}{d x} (- \frac{1}{3} (x^{- 3} - x^{6}))

\frac{\partial}{\partial x} (x cos (x y) - 2 y)