What is the derivative of arccot(3x) ?

The derivative of arccot(3x) is -3/(9x^2+1)

What is the first derivative of arccot(3x) ?

The first derivative of arccot(3x) is -3/(9x^2+1)

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derivative of

arccot (3 x)

- \frac{3}{9 x ^{2} + 1}

Solution steps

\frac{d}{d x} (arccot (3 x))

Apply the chain rule:

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

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

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

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

Simplify

- \frac{1}{( 3 x ) ^{2} + 1} \cdot 3 : - \frac{3}{9 x ^{2} + 1}

= - \frac{3}{9 x ^{2} + 1}

What is the derivative of arccot(3x) ?
The derivative of arccot(3x) is -3/(9x^2+1)
What is the first derivative of arccot(3x) ?
The first derivative of arccot(3x) is -3/(9x^2+1)