derivative of 2/(1+x^3)

Lösung

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

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

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})^{- 1})

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= - \frac{6 x ^{2}}{( 1 + x ^{3} ) ^{2}}

in v erse l a pl a ce \frac{s ^{2}}{( s - 3 ) ^{2}}

s l o p e 2 + 5 x^{2} - 2 x^{3}

t an g e n t f (x) = x^{2} - 7 x + 7, at x = 6

t an g e n t f (x) = (6 - 3 x) (6 + 3 x), at x = 3

\int_{- 0.5}^{0.5} 1.5 x^{2} d x