derivative of 12arccot(ax^2)

Lösung

\frac{d}{d x} (12 arccot (a x^{2}))

- \frac{24 a x}{a ^{2} x ^{4} + 1}

Schritte zur Lösung

\frac{d}{d x} (12 arccot (a x^{2}))

Entferne die Konstante:

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

= 12 \frac{d}{d x} (arccot (a x^{2}))

Wende die Kettenregel an:

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

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

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

= 12 (- \frac{1}{( a x ^{2} ) ^{2} + 1} \cdot 2 a x)

Vereinfache

12 (- \frac{1}{( a x ^{2} ) ^{2} + 1} \cdot 2 a x) : - \frac{24 a x}{a ^{2} x ^{4} + 1}

= - \frac{24 a x}{a ^{2} x ^{4} + 1}

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