derivative of arctan(x)^(1/2)

[dmha8376]

I think I have this pretty much solved. In class, we went over derivatives of arctan already.
I know it's 1/x^2+1.

So far, my answer is:
1/2(1/x^2+1)^(-1/2)

I'm just wondering if the chain rule applies here... since the inside function is not solved yet?
So would my answer be:

1/2(1/x^2+1)^(-1/2) x (2x)?

Or would I leave it alone?

 

[royhaas]

Your function, as written, is \(\displaystyle \sqrt{arctan(x)}\), not \(\displaystyle arctan(\sqrt{x})\). In either case you have not applied the chain rule correctly.

 

[Deleted member 4993]

I think I have this pretty much solved. In class, we went over derivatives of arctan already.
I know it's 1/x^2+1. <<<< that is not correct

d/dx [arctan(x)] = 1/(1+x[sup:6di1frwy]2[/sup:6di1frwy])

without the parenthesis it says something different.

Similarly,

do you want to find the derivative of

?[arctan(x)] or

arctan(?x)

Use parenthesis to group operations (following PEMDAS) - so that we understand the problem

So far, my answer is:
1/2(1/x^2+1)^(-1/2)

I'm just wondering if the chain rule applies here... since the inside function is not solved yet?
So would my answer be:

1/2(1/x^2+1)^(-1/2) x (2x)?

Or would I leave it alone?