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Beliebt Rechnen >

derivative y= 1/((x^2-1)(x^2+3x+3))

Lösung

ableitung von

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

Lösung

- \frac{4 x ^{3} + 9 x ^{2} + 4 x - 3}{( x ^{2} - 1 ) ^{2} ( x ^{2} + 3 x + 3 ) ^{2}}

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} ((x^{2} - 1) (x^{2} + 3 x + 3)) = 4 x^{3} + 9 x^{2} + 4 x - 3

= - \frac{1}{( ( x ^{2} - 1 ) ( x ^{2} + 3 x + 3 ) ) ^{2}} (4 x^{3} + 9 x^{2} + 4 x - 3)

Vereinfache

- \frac{1}{( ( x ^{2} - 1 ) ( x ^{2} + 3 x + 3 ) ) ^{2}} (4 x^{3} + 9 x^{2} + 4 x - 3) : - \frac{4 x ^{3} + 9 x ^{2} + 4 x - 3}{( x ^{2} - 1 ) ^{2} ( x ^{2} + 3 x + 3 ) ^{2}}

= - \frac{4 x ^{3} + 9 x ^{2} + 4 x - 3}{( x ^{2} - 1 ) ^{2} ( x ^{2} + 3 x + 3 ) ^{2}}

Graph

Beliebte Beispiele

derivative of x^{9/4}

\frac{d}{d x} (x^{\frac{9}{4}})

derivative f(θ)=sqrt(11θ)

d er i v a t i v e f (θ) = 11 θ

f(s)=sqrt((s^2+1)/(s^2+4))

f (s) = \frac{s ^{2} + 1}{s ^{2} + 4}

integral from 1 to 4 of x-(x-2)^2

\int_{1}^{4} x - (x - 2)^{2} d x

limit as x approaches 2 of sqrt((6-x)-2)

x \to 2 lim ((6 - x) - 2)