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Beliebt Rechnen >

derivative 1/3 (x^2-2)^{3/2}

Lösung

ableitung von

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

Lösung

x (x^{2} - 2)^{\frac{1}{2}}

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

integral of ((x^2-x+36))/(x^3+6x)

\int \frac{( x ^{2} - x + 36 )}{x ^{3} + 6 x} d x

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t an g e n t y = 2 sin (x), (\frac{π}{6}, 1)

derivative 1-(1-0.01x)^3

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sum from n=1 to infinity of n^{3/4}

n = 1 \sum \infty n^{\frac{3}{4}}

integral of 90x^2sin(2+6x^3)

\int 90 x^{2} sin (2 + 6 x^{3}) d x