derivative sqrt((y+1)/(y-1))

Lösung

ableitung von

\frac{y + 1}{y - 1}

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

Schritte zur Lösung

\frac{d}{d y} (\frac{y + 1}{y - 1})

Wende die Kettenregel an:

\frac{1}{2 \frac{y + 1}{y - 1}} \frac{d}{d y} (\frac{y + 1}{y - 1})

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

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

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

Vereinfache

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

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

x \to \infty lim (1^{x})

\frac{d}{d x} (3 x + 16)

\frac{d}{d x} (- csc (x) - cos (x))

t an g e n t f (x) = x + \frac{1}{x}, at x = 2

\frac{d}{d t} (\frac{3}{t})