What is the derivative of arccot(x/9) ?

The derivative of arccot(x/9) is -9/(x^2+81)

What is the first derivative of arccot(x/9) ?

The first derivative of arccot(x/9) is -9/(x^2+81)

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derivative of

arccot (\frac{x}{9})

- \frac{9}{x ^{2} + 81}

Solution steps

\frac{d}{d x} (arccot (\frac{x}{9}))

Apply the chain rule:

- \frac{1}{( \frac{x}{9} ) ^{2} + 1} \frac{d}{d x} (\frac{x}{9})

= - \frac{1}{( \frac{x}{9} ) ^{2} + 1} \frac{d}{d x} (\frac{x}{9})

\frac{d}{d x} (\frac{x}{9}) = \frac{1}{9}

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

Simplify

- \frac{1}{( \frac{x}{9} ) ^{2} + 1} \cdot \frac{1}{9} : - \frac{9}{x ^{2} + 81}

= - \frac{9}{x ^{2} + 81}

What is the derivative of arccot(x/9) ?
The derivative of arccot(x/9) is -9/(x^2+81)
What is the first derivative of arccot(x/9) ?
The first derivative of arccot(x/9) is -9/(x^2+81)