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Beliebt Rechnen >

derivative (a+b/(x^2))^3

Lösung

ableitung von

(a + \frac{b}{x ^{2}})^{3}

Lösung

- \frac{6 b ( a x ^{2} + b ) ^{2}}{x ^{7}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

3 (a + \frac{b}{x ^{2}})^{2} (- \frac{2 b}{x ^{3}}) : - \frac{6 b ( a x ^{2} + b ) ^{2}}{x ^{7}}

= - \frac{6 b ( a x ^{2} + b ) ^{2}}{x ^{7}}

Graph

Beliebte Beispiele

f(x)=e^{4x}+4e^{4x}x

limit as x approaches infinity of (ln^3(x))/(100\sqrt[3]{x)}

integral of 12xe^{-3x}

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tangent f(x)=2+1/x ,(4,2.25)