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Beliebt Rechnen >

derivative of x\sqrt[3]{x^2}

Lösung

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

Lösung

3 x^{2} + \frac{2 x ^{\frac{2}{3}}}{3}

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = 3 x^{2}

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

\frac{d x}{d x} = 1

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

= 1 \cdot 3 x^{2} + \frac{2}{3 x ^{\frac{1}{3}}} x

Vereinfache

1 \cdot 3 x^{2} + \frac{2}{3 x ^{\frac{1}{3}}} x : 3 x^{2} + \frac{2 x ^{\frac{2}{3}}}{3}

= 3 x^{2} + \frac{2 x ^{\frac{2}{3}}}{3}

Graph

Beliebte Beispiele

f^'(x)=x^2-x,f(3)= 19/2

f^{^{'}} (x) = x^{2} - x, f (3) = \frac{19}{2}

limit as x approaches 0 of (sin(10x))/(sin(3x))

x \to 0 lim (\frac{sin ( 10 x )}{sin ( 3 x )})

integral of sin(3x)cos(2x)

\int sin (3 x) cos (2 x) d x

integral of (sec(1/x)tan(1/x))/(x^2)

\int \frac{sec ( \frac{1}{x} ) tan ( \frac{1}{x} )}{x ^{2}} d x

derivative of (94x/(99x-94))

\frac{d}{d x} (\frac{94 x}{99 x - 94})