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Beliebt Rechnen >

derivative (x^3)/(x+1)

Lösung

ableitung von

\frac{x ^{3}}{x + 1}

Lösung

\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}}

Graph

Beliebte Beispiele

integral of 18e^x

\int 18 e^{x} d x

integral from 0 to 64 of 5/(x^{2/3)}

\int_{0}^{64} \frac{5}{x ^{\frac{2}{3}}} d x

integral from-pi/4 to 0 of 8sec^3(x)

\int_{- \frac{π}{4}}^{0} 8 sec^{3} (x) d x

laplacetransform 15t^3

l a pl a ce t r an s f or m 15 t^{3}

f(x)=sin(xcos(x))

f (x) = sin (x cos (x))