$\displaystyle

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

$

what i have so far is, leaving the x on the left aside for abit.

$\displaystyle

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

$

then

$\displaystyle

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

$

then

$\displaystyle

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

$

now what do i do with the x? (thats if my calculations are correct)