derivative of trig of a ln of a sqare root questions

$\displaystyle y=tan(ln(sqrt(x^2 +1)))$

find y'

I got

$\displaystyle sec^2x(ln(sqrt(x^2+1))) * [1/2(x^2+1)] ^ -0.5 /sqrt(x^2+1) $

which is multiplied by the derivative of sqrt (x^2-1) and then multiplied by 2x (the derivative of x^2)

is there an error in there?

Re: derivative of trig of a ln of a sqare root questions

$\displaystyle y = \tan[\ln{\sqrt{x^2+1}}] = \tan \left[\frac{1}{2}\ln(x^2+1)\right]$

$\displaystyle \frac{dy}{dx} = \sec^2 \left[\frac{1}{2}\ln(x^2+1) \right] \cdot \frac{x}{x^2+1}$