derivative f(x)=(x^3)/(x-1)

Lösung

ableitung von

f (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}}

n = 0 \sum \infty (\frac{2}{7})^{\frac{n}{2}}

y^{^{'''}} + 2 y^{^{''}} - y^{^{'}} - 2 y = 0

\int_{0}^{2} 1 + 16 x^{2} d x

x \to π lim (5 \frac{x - π}{x + π})

s im pl i f y 2 π \frac{x}{g}