(\partial)/(\partial x)(-1/((1+x)^2))

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

f (x) = π x^{2}

d er i v a t i v e cos (a^{9} + x^{9})

x \to 0 lim (cos (\frac{1}{x}))

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

\int (e^{x})^{3} d x