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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

x \to + 4 lim (3)

y^{^{''}} - 3 y^{^{'}} + 4 y = 0

\frac{d}{d x} (\frac{( 4 x - 2 ) ^{4}}{3 x ^{2} + 7})

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

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