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

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

\frac{\partial}{\partial x} (2 x y)

d er i v a t i v e f (x) = (9 - 6 x^{2})^{2}

(2 x + y + 1) y^{^{'}} = 1

(x^{2} - 1)^{^{'}}

\frac{d}{d x} f (x) = - 9