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derivative of arctan(x/a)

Solution

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

Solution

\frac{a}{x ^{2} + a ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{a}{x ^{2} + a ^{2}}

Graph

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x \to 0 + lim (- ln (x))

Frequently Asked Questions (FAQ)

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