How Do You Derive tan^(-1)(sqrt(8x^2-1))?

[cemar.]

Derivative arctan function! Please help!

Find the derivative of tan^(-1)(sqrt(8x^2-1)))

I knwo that the derivative of tan^(-1)(x) is 1/(1+x^2) and that you are supposed to use the chain rule twice but i cannot seem to get the right answer.
If some one could please show me the steps i could figure out where i went wrong! Thanks!

 

[Dick]

Show us what you did first. The first chain rule involves the tan^(-1) and the second involves the sqrt.

 

[cemar.]

okay what i did was

1. f(x) = arctan((sqrt(8x^2-1)))

2. f'(x) = ((1/(1+(8x^2-1))) * (1/2)(8x^2-1)^(-1/2) * 16x

3. = 16x/((8x^2) * 2 * sqrt(8x^2-1))

4. = 1/(x(sqrt(8x^2-1))

 

[Dick]

I believe that is correct.

 

[cemar.]

really?! That would explain why i was so confused. These online assignments are no fun. I guess i just have to work on submitting my answers properly. Ill just double check (again).
and thank you so much! I have been tearing my hair out over this for about an hour now trying to figure out where i went wrong.