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

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

t an g e n t y = (s - 4) (s^{2} - 3), (1, 6)

\frac{d}{d x} (\frac{x ^{4}}{4})

\int_{0}^{\frac{π}{20}} cos (5 x) d x

x \to 0 + lim (\frac{7}{x ^{3} + 2 x ^{2}})

\frac{d}{d x} (e^{2 x + l n (x)})