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