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

Lösung

ableitung von

\frac{1}{x ^{2} + 3 x - 1}

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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

\int_{0}^{π} t \cdot sin (3 t) d t

n = 0 \sum \infty \frac{2}{5 ^{n - 1}}

t an g e n t y = sin (sin (x)), (3 π, 0)

(- x)^{^{'}}