Find the derivative of f(x)=x+x+xf(x) = \sqrt{x+\sqrt{x+\sqrt{x}}}f(x)=x+x+x.
1+12x+14xx+x2x+x+x\frac{1 + \frac{1}{2\sqrt{x}} + \frac{1}{4\sqrt{x}\sqrt{x+\sqrt{x}}}}{2\sqrt{x+\sqrt{x+\sqrt{x}}}}2x+x+x1+2x1+4xx+x1
12x+x+x\frac{1}{2\sqrt{x+\sqrt{x+\sqrt{x}}}}2x+x+x1
111
2x2\sqrt{x}2x