How do you differentiate $arctan (\frac{x}{a})$ $arctan(x/a)$ ?

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Answer 1 · 2016-08-20T11:36:23

$= \frac{a}{x^{2} + a^{2}}$ $= a/ (x^2 + a^2)$

$y = arctan (\frac{x}{a})$ $y = arctan (x/a)$

$tan y = \frac{x}{a}$ $tan y = x/a$

$sec^2 y \ y' = 1/a$

$y' = 1/(a sec^2 y)$

$= 1/(a (tan^2 y + 1)$

$= 1/(a ((x/a)^2 + 1)$

$= a/ (x^2 + a^2)$

How do you differentiate arctan(x/a)arctan(xa)arctan(x/a)?