derivative of ((x-2/(2x+1))^9)

Lösung

\frac{d}{d x} ((\frac{x - 2}{2 x + 1})^{9})

\frac{45 ( x - 2 ) ^{8}}{( 2 x + 1 ) ^{10}}

Schritte zur Lösung

\frac{d}{d x} ((\frac{x - 2}{2 x + 1})^{9})

Wende die Kettenregel an:

9 (\frac{x - 2}{2 x + 1})^{8} \frac{d}{d x} (\frac{x - 2}{2 x + 1})

= 9 (\frac{x - 2}{2 x + 1})^{8} \frac{d}{d x} (\frac{x - 2}{2 x + 1})

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

= 9 (\frac{x - 2}{2 x + 1})^{8} \frac{5}{( 2 x + 1 ) ^{2}}

Vereinfache

9 (\frac{x - 2}{2 x + 1})^{8} \frac{5}{( 2 x + 1 ) ^{2}} : \frac{45 ( x - 2 ) ^{8}}{( 2 x + 1 ) ^{10}}

= \frac{45 ( x - 2 ) ^{8}}{( 2 x + 1 ) ^{10}}

x \to 3 lim (\frac{x - 3}{x - 3})

\int ln (3 x + 5) d x

d er i v a t i v e f (x) = 2 x^{2} - 5 x + 3

\frac{d}{d x} ((a x^{2} + b x + c) e^{\frac{- x}{2}})

d er i v a t i v e \frac{1}{3 s ^{2}} - \frac{5}{4 s ^{3}}