What is the derivative of #y= arctan( x/2)#?

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Answer 1 · 2016-03-22T07:07:28

#dy/dx=2/(x^2+4)#

#y = arctan(x/2)#

#=> tan(y) = x/2#

#=> d/dxtan(y) = d/dx x/2#

#=> sec^2(y)dy/dx = 1/2#

#:. dy/dx = 1/(2sec^2(y))#

#= 1/(2*(x^2+4)/4)#
(To see why, try drawing a right triangle with angle #y# such that #tan(y) = x/2#. What does #sec^2(y)# equal?)

#=2/(x^2+4)#