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Popular Calculus >

derivative of arctan(x/6)

Solution

derivative of

arctan (\frac{x}{6})

Solution

\frac{6}{x ^{2} + 36}

Solution steps

\frac{d}{d x} (arctan (\frac{x}{6}))

Apply the chain rule:

\frac{1}{( \frac{x}{6} ) ^{2} + 1} \frac{d}{d x} (\frac{x}{6})

= \frac{1}{( \frac{x}{6} ) ^{2} + 1} \frac{d}{d x} (\frac{x}{6})

\frac{d}{d x} (\frac{x}{6}) = \frac{1}{6}

= \frac{1}{( \frac{x}{6} ) ^{2} + 1} \cdot \frac{1}{6}

Simplify

\frac{1}{( \frac{x}{6} ) ^{2} + 1} \cdot \frac{1}{6} : \frac{6}{x ^{2} + 36}

= \frac{6}{x ^{2} + 36}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of arctan(x/6) ?
The derivative of arctan(x/6) is 6/(x^2+36)
What is the first derivative of arctan(x/6) ?
The first derivative of arctan(x/6) is 6/(x^2+36)