I need to find the derivative of the following function.

$\displaystyle y=sqrt{x+sqrt{x+sqrt{x}} $

[tex] i think this can be simplified to $\displaystyle sqrt{x} + (sqrt{x}(sqrt{x}+1))^1/4 $

so would it be reasonable to use the product and chain rule to solve the derivative of the 2nd part of the equation and just generally derive the 1st part?