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

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Answer 1 · 2016-08-20T11:36:23

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

#y = arctan (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)#