derivative (2/(sqrt(x))-1)^{-1}

Lösung

ableitung von

(\frac{2}{x} - 1)^{- 1}

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

x \to 0 lim (ln (\frac{x}{3}) + x^{2} - 8)

l a pl a ce t r an s f or m \frac{2}{3} t^{3} e^{- 8 t}

\frac{d}{d x} (3 cos (x) - sin (x))

\int \frac{x + 9}{16 - ( x - 4 ) ^{2}} d x

\int (sin (x))^{11} (cos (x))^{5} d x