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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Vereinfache

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

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

integral of cos^2(3t)

\int cos^{2} (3 t) d t

(\partial)/(\partial x)((x+y)/(x^2+y^2))

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

integral of (x^2+x-2)

\int (x^{2} + x - 2) d x

derivative of arctan(1/2 x)

\frac{d}{d x} (arctan (\frac{1}{2} x))

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

\int \frac{x + 3}{x ^{2} + 1} d x