If $y = \sqrt{\log(x^2+1)+\sqrt{\log(x^2+1)+\sqrt{\log(x^2+1)+...}}}$, $|x|<1$, then $\frac{dy}{dx} =$
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For functions defined by infinite nested expressions like $y = \sqrt{f(x)+\sqrt{f(x)+...}}$, you can write them as a simple equation, $y = \sqrt{f(x)+y}$. Squaring both sides gives $y^2 = f(x)+y$, which can then be easily differentiated using implicit differentiation.