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

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

l a pl a ce t r an s f or m e^{- 2 t} sin (t)

x \to a lim (\frac{3}{0})

d er i v a t i v e \frac{- x ^{2} - 4}{( x ^{2} - 4 ) ^{2}}

n = 0 \sum \infty \frac{1}{( 1 + n ^{2} )}

n = 0 \sum \infty \frac{1}{7 ^{n}}