derivative of 2/((1+x^3))

Lösung

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

- \frac{6}{( 1 + x ) ^{4}}

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

- \frac{3}{( 1 + x ) ^{4}} \frac{d}{d x} (1 + x)

= - \frac{3}{( 1 + x ) ^{4}} \frac{d}{d x} (1 + x)

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

= 2 (- \frac{3}{( 1 + x ) ^{4}} \cdot 1)

Vereinfache

2 (- \frac{3}{( 1 + x ) ^{4}} \cdot 1) : - \frac{6}{( 1 + x ) ^{4}}

= - \frac{6}{( 1 + x ) ^{4}}

t an g e n t y = x^{2} + x, (1, 2)

a re a x^{2} + 12 x, 3 x^{2} + 10, 1, 4

y^{^{''}} - 4 y^{^{'}} + 4 y = 3 x^{2} + 2 x e^{2 x}

n = 9 \sum \infty e^{3 - 2 n}

in v erse l a pl a ce \frac{1}{1 + x}