# Do not FOIL

**Calculus**Level 3

Given the nested radical equation...

\[ y = \sqrt{\dfrac {x}{2} + \sqrt{\dfrac {x}{2^3} + \sqrt{\dfrac {x}{2^7} + \sqrt{\dfrac {x}{2^{15}} + \sqrt{\dfrac {x}{2^{31}} + \sqrt{\dfrac {x}{2^{63}} + \ldots }}}}} } \]

...use the parameter \( \dfrac {\mathrm{d}y }{\mathrm{d}x} \geq 0\) to find \( \dfrac {\mathrm{d}y }{\mathrm{d}x}\) at the \(x\)-value given below. (Round your answer to two decimal places).

\[ x =\sqrt{2\sqrt{16 \sqrt{2\sqrt{16 \sqrt{2\sqrt{16 \ldots }}}}}} \]

###### This problem is original.

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