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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

l a pl a ce t r an s f or m 12 t^{3} - t^{2}

\frac{d}{d x} (2 x - \frac{4}{x})

\int \frac{x ^{2}}{81 + x ^{2}} d x

\int_{0}^{1} sin (π \cdot x) d x

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