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Beliebt Rechnen >

derivative of xsqrt(x)+x^2sqrt(x)

Lösung

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

Lösung

\frac{3 x + 5 x ^{\frac{3}{2}}}{2}

Schritte zur Lösung

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

Vereinfache

x x + x^{2} x : x^{\frac{3}{2}} + x^{\frac{5}{2}}

= \frac{d}{d x} (x^{\frac{3}{2}} + x^{\frac{5}{2}})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x^{\frac{3}{2}}) + \frac{d}{d x} (x^{\frac{5}{2}})

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

\frac{d}{d x} (x^{\frac{5}{2}}) = \frac{5 x ^{\frac{3}{2}}}{2}

= \frac{3 x}{2} + \frac{5 x ^{\frac{3}{2}}}{2}

Wende Regel an

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{3 x + 5 x ^{\frac{3}{2}}}{2}

Graph

Beliebte Beispiele

derivative 4e^{4x}cos(5x)

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sum from n=0 to infinity of 4546644

n = 0 \sum \infty 4546644

limit as x approaches 3 of (x^x+x)^x

x \to 3 lim ((x^{x} + x)^{x})

(ln (\frac{x}{3}))^{^{'}}