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Popular >

derivative of arccot(x/5)

Solution

\frac{d}{d x} (arccot (\frac{x}{5}))

Solution

- \frac{5}{x ^{2} + 25}

Solution steps

\frac{d}{d x} (arccot (\frac{x}{5}))

Apply the chain rule:

- \frac{1}{( \frac{x}{5} ) ^{2} + 1} \frac{d}{d x} (\frac{x}{5})

= - \frac{1}{( \frac{x}{5} ) ^{2} + 1} \frac{d}{d x} (\frac{x}{5})

\frac{d}{d x} (\frac{x}{5}) = \frac{1}{5}

= - \frac{1}{( \frac{x}{5} ) ^{2} + 1} \cdot \frac{1}{5}

Simplify

- \frac{1}{( \frac{x}{5} ) ^{2} + 1} \cdot \frac{1}{5} : - \frac{5}{x ^{2} + 25}

= - \frac{5}{x ^{2} + 25}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of arccot(x/5) ?
The derivative of arccot(x/5) is -5/(x^2+25)
What is the first derivative of arccot(x/5) ?
The first derivative of arccot(x/5) is -5/(x^2+25)