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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

in v erse l a pl a ce \frac{s - 1}{s ^{2} + 4 s + 5}

\frac{\partial}{\partial x} (e^{x} cos (x))

d er i v a t i v e f (x) = x^{2} + 5

\frac{d}{d x} (cos (2 x + π))

d er i v a t i v e (9 - 2 x^{3})^{3}