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

Lösung

ableitung von

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

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

Schritte zur Lösung

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

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

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

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

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

Vereinfache

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

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

f (x) = sin (9 ln (x))

x \to 8 lim (x^{(\frac{2}{3})})

x^{^{''}} = k^{2} x

\frac{\partial}{\partial x} (x \cdot sin (x^{2} - y^{2}))

\int_{- 2}^{2} \frac{1}{∣ 2 x ∣} d x