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Popular Calculus >

derivative of arccot(x/2)

Solution

\frac{d}{d x} (arccot (\frac{x}{2}))

Solution

- \frac{2}{x ^{2} + 4}

Solution steps

\frac{d}{d x} (arccot (\frac{x}{2}))

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x}{2}) = \frac{1}{2}

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

Simplify

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

= - \frac{2}{x ^{2} + 4}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of arccot(x/2) ?
The derivative of arccot(x/2) is -2/(x^2+4)
What is the first derivative of arccot(x/2) ?
The first derivative of arccot(x/2) is -2/(x^2+4)