What is the first derivative and nth derivative of the following function $ y = \sqrt {2 +\sqrt {3 + \sqrt{x}}}$ What is the first derivative and nth derivative of the following function $ y = \sqrt {2 +\sqrt {3 + \sqrt {x}}}$ 
I think taking the ln for both sides will remove the first square root only?
Could anyone give me a hint ?  

Alternative approach (same answer) ...
$y^2 = 2+ \sqrt{3+\sqrt{x}}$
$\Rightarrow y^2-2=\sqrt{3 + \sqrt{x}}$
$\Rightarrow y^4-4y^2+4=3+\sqrt{x}$
$\Rightarrow 4y^3\frac{dy}{dx} - 8y\frac{dy}{dx} = \frac{1}{2\sqrt{x}}$
$\Rightarrow \frac{dy}{dx} = \frac{1}{8y(y^2-2)\sqrt{x}}$
