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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

limit as x approaches 0 of 4x^2-2x+3

x \to 0 lim (4 x^{2} - 2 x + 3)

integral of x/(10^x)

\int \frac{x}{1 0 ^{x}} d x

fläche 10-7x,x^2-20,0

a re a 10 - 7 x, x^{2} - 20, 0

derivative of x^6{f}(x)

\frac{d}{d x} (x^{6} f (x))

f (u) = ln (u)