derivative of 1/(1+2/x)

Lösung

\frac{d}{d x} (\frac{1}{1 + \frac{2}{x}})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{1 + \frac{2}{x}})

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (0.8 cos (x) + 0.5 sin (2 x))

\frac{d}{d x} (\frac{98}{( 7 x - 13 ) ^{3}})

d er i v a t i v e x sin (3 x)

\int \frac{1}{( 10 x - 1 ) ^{6}} d x

d er i v a t i v e \frac{7 ^{x}}{x ^{3}}