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Beliebt Rechnen >

derivative of 4/((x+1^2))

Lösung

\frac{d}{d x} (\frac{4}{( x + 1 ) ^{2}})

Lösung

- \frac{8}{( x + 1 ) ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{4}{( x + 1 ) ^{2}})

Entferne die Konstante:

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

= 4 \frac{d}{d x} (\frac{1}{( x + 1 ) ^{2}})

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

4 (- \frac{2}{( x + 1 ) ^{3}} \cdot 1) : - \frac{8}{( x + 1 ) ^{3}}

= - \frac{8}{( x + 1 ) ^{3}}

Graph

Beliebte Beispiele

integral of (2/x-3/(x^4))

\int (\frac{2}{x} - \frac{3}{x ^{4}}) d x

steigung y= 2/x

s l o p e y = \frac{2}{x}

integral of x^{1/2}sqrt(1+x^{1/2)}

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

integral of 10^{2x}

\int 1 0^{2 x} d x

limit as x approaches 0 of sqrt(x+3)

x \to 0 lim (x + 3)