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Beliebt Rechnen >

derivative of 6/((1+x^4))

Lösung

\frac{d}{d x} (\frac{6}{( 1 + x ) ^{4}})

Lösung

- \frac{24}{( 1 + x ) ^{5}}

Schritte zur Lösung

\frac{d}{d x} (\frac{6}{( 1 + x ) ^{4}})

Entferne die Konstante:

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

= 6 \frac{d}{d x} (\frac{1}{( 1 + x ) ^{4}})

Wende Exponentenregel an:

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

= 6 \frac{d}{d x} ((1 + x)^{- 4})

Wende die Kettenregel an:

- \frac{4}{( 1 + x ) ^{5}} \frac{d}{d x} (1 + x)

= - \frac{4}{( 1 + x ) ^{5}} \frac{d}{d x} (1 + x)

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

= 6 (- \frac{4}{( 1 + x ) ^{5}} \cdot 1)

Vereinfache

6 (- \frac{4}{( 1 + x ) ^{5}} \cdot 1) : - \frac{24}{( 1 + x ) ^{5}}

= - \frac{24}{( 1 + x ) ^{5}}

Graph

Beliebte Beispiele

derivative of (6x^3-2/(x^2-4))

\frac{d}{d x} (\frac{6 x ^{3} - 2}{x ^{2} - 4})

tangent f(x)=x^2+x

t an g e n t f (x) = x^{2} + x

integral of sec(5x)tan(5x)

\int sec (5 x) tan (5 x) d x

derivative of sec(1/(sqrt(x)))

\frac{d}{d x} (sec (\frac{1}{x}))

limit as x approaches 1 of-1

x \to 1 lim (- 1)