derivative of (10x^3/(x^2-1))

Lösung

\frac{d}{d x} (\frac{10 x ^{3}}{x ^{2} - 1})

\frac{10 ( x ^{4} - 3 x ^{2} )}{( x ^{2} - 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{10 x ^{3}}{x ^{2} - 1})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 10 \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}}

= 10 \cdot \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

= 10 \cdot \frac{3 x ^{2} ( x ^{2} - 1 ) - 2 x x ^{3}}{( x ^{2} - 1 ) ^{2}}

Vereinfache

10 \cdot \frac{3 x ^{2} ( x ^{2} - 1 ) - 2 x x ^{3}}{( x ^{2} - 1 ) ^{2}} : \frac{10 ( x ^{4} - 3 x ^{2} )}{( x ^{2} - 1 ) ^{2}}

= \frac{10 ( x ^{4} - 3 x ^{2} )}{( x ^{2} - 1 ) ^{2}}

\int \frac{( x ^{2} - 16 )}{x} d x

\frac{d}{d x} (arctan (ln (x)))

\frac{\partial}{\partial x} (x^{4} y^{8} + 4 x^{5} y)

d er i v a t i v e ln (\frac{x}{x ^{2} + 2})

\frac{d}{d x} (5 lo g_{2} (x))