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Beliebt Rechnen >

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

Lösung

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

Lösung

- \frac{6 x}{( x ^{2} + 1 ) ^{4}}

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

- \frac{3}{( x ^{2} + 1 ) ^{4}} \cdot 2 x : - \frac{6 x}{( x ^{2} + 1 ) ^{4}}

= - \frac{6 x}{( x ^{2} + 1 ) ^{4}}

Graph

Beliebte Beispiele

integral of (e^{3x})/(e^{3x)+9}

\int \frac{e ^{3 x}}{e ^{3 x} + 9} d x

integral from 0 to 1 of pi(6-3/2 x)^2

\int_{0}^{1} π (6 - \frac{3}{2} x)^{2} d x

inverselaplace 2/(s^2+s)

in v erse l a pl a ce \frac{2}{s ^{2} + s}

y^{''}+9y=3cos(2x)+3

y^{^{''}} + 9 y = 3 cos (2 x) + 3

integral of sqrt(9-x^2)(-2x)

\int 9 - x^{2} (- 2 x) d x