# derivative of trig of a ln of a sqare root questions

• October 31st 2012, 10:26 AM
kingsolomonsgrave
derivative of trig of a ln of a sqare root questions
$y=tan(ln(sqrt(x^2 +1)))$

find y'

I got

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

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?
• October 31st 2012, 10:51 AM
skeeter
Re: derivative of trig of a ln of a sqare root questions
$y = \tan[\ln{\sqrt{x^2+1}}] = \tan \left[\frac{1}{2}\ln(x^2+1)\right]$

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