<s>[INST] 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 ?  
 [/INST] First of all. Use chain rule. I'd recommend learning something new instead of relying on app.(personal opinion)
$$\frac{dy}{dx}=\frac{1}{2\sqrt{2+\sqrt{3+\sqrt{x}}}}.\frac{d\sqrt{3+\sqrt{x}}}{dx}$$
$$\frac{dy}{dx}=\frac{1}{2\sqrt{2+\sqrt{3+\sqrt{x}}}}.\frac{1}{2\sqrt{3+\sqrt{x}}}\frac{d\sqrt{x}}{dx}$$
$$\frac{dy}{dx}=\frac{1}{2\sqrt{2+\sqrt{3+\sqrt{x}}}}.\frac{1}{2\sqrt{3+\sqrt{x}}}\frac{1}{2\sqrt{x}}$$
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