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

1 Answer
Apr 4, 2018

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

Explanation:

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)#