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

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Vereinfache

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

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

x \to 1 lim (x ln (x))

\int \frac{1}{x + 2} d x

\frac{d}{d x} (2 - 5 x)

t a y l or ln ((\frac{x}{2})^{2} + 4^{2})

\int_{- 2}^{2} \frac{1}{1 + x ^{2}} d x