Thread: Derivative of an Inverse function

1. Derivative of an Inverse function

$
y =\tan^{-1}\left(\sqrt{4 x^2-1}\right)
$
Find the Derivative.

I just realized an hour ago my assignments due, and I'm not quite sure to how to do the question so if anyone can explain what to do, that'd be awsome. I have the proofs, I just dont know how to use them.

2. Originally Posted by Lolcats
$
y =\tan^{-1}\left(\sqrt{4 x^2-1}\right)
$
Find the Derivative.

I just realized an hour ago my assignments due, and I'm not quite sure to how to do the question so if anyone can explain what to do, that'd be awsome. I have the proofs, I just dont know how to use them.
Apply the following:
If $y=tan^{-1}( f(x) )$
then $y'=\frac{1}{1+(f(x))^2} f'(x)$

3. k so would the answer be
1/(1+((4x^(2)-1)^1/2)2) x (1/2) (4x^(2)-1)^(-1/2) (8x)?

4. do the following:
1)make a substitution:2x=sec(theta).
2)find dx/d(theta).
3)find dy/d(theta).
4)divide to get dy/dx.
5)get the answer in terms of theta.
6)make the back substitution.