Inverse Trig Function Help

Question

I do not know what I'm doing wrong for this question, but apparently I'm getting the wrong answer. The question is differentiate $$y=\operatorname {arcsec}(\sqrt{x^2+2})$$

I have attached my work here

Can someone please explain to me what I'm doing wrong?

Answer 1

HINT : $$(\sec^{-1}(x))'=\frac{1}{x^2\sqrt{1-\frac{1}{x^2}} }$$

Answer 2

$$y'=\frac{x}{\left(x^2+2\right)\sqrt{x^2+1} }$$

Hope it helps