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

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

t a y l or e^{- x^{2}} 1

\int sin (x) + x d x

\int \frac{36}{x} d x

\int 18 x^{5} d x

\frac{d ^{4}}{d x ^{4}} (17 e^{x^{2}})