please help with derivatives of inverse trig functions

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.

If the chain rule is the case, what happens when there is a constant, such as 29 instead of x, so the problem is 29 arctan (squareroot of x).

Would it thus have a + 29 arctan (square root of x)?