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

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Answer 1 · 2018-04-04T03:41:03

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

In general,

#d/dxarctanx=1/(1+x^2)#

So, this problem will also require application of the Chain Rule:

#d/dxarctan(x/2)=1/(1+(x/2)^2)*d/dx(x/2)#

#d/dxarctan(x/2)=1/(1+x^2/4)*1/2#

#d/dxarctan(x/2)=1/(2+x^2/2)#

We'll want to get rid of that fraction in the denominator. It doesn't look very good.

#d/dxarctan(x/2)=1/((4+x^2)/2)#

Finally,

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