What is the derivative of 12arccot(ax^2) ?

The derivative of 12arccot(ax^2) is -(24ax)/(a^2x^4+1)

What is the first derivative of 12arccot(ax^2) ?

The first derivative of 12arccot(ax^2) is -(24ax)/(a^2x^4+1)

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

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

- \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)

Simplify

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}

What is the derivative of 12arccot(ax^2) ?
The derivative of 12arccot(ax^2) is -(24ax)/(a^2x^4+1)
What is the first derivative of 12arccot(ax^2) ?
The first derivative of 12arccot(ax^2) is -(24ax)/(a^2x^4+1)