...the problem is x arctan squareroot(x)

i solve it out and got (square root of x)/2(1+x)

However, the book answer gives it as my answer + arctan(square root of x)

How did the book get the + arctan(squre root of x)

I went through my work 4 times and I can't find out why. Unless the x in fron of arctan square root of x plays a role via chain rule.

product rule ...