$\displaystyle

y = x\sqrt{x^2+1}

$

$\displaystyle

f (x) = x,

g (x) = \sqrt{x^2 + 1}

$

$\displaystyle

f '(x) = 1,

g '(x) = \frac{x}{\sqrt{x^2 + 1}}

$

using the product rule:

$\displaystyle

= (\sqrt{x^2 + 1}) + x(\frac{x}{\sqrt{x^2 + 1}})

$

this correcT? thank you