[Math] Find the derivative of $y=\sqrt{1+\sqrt x}\,$

Question

Find the derivative of $y=\sqrt{1+\sqrt{x}}$

I know it comes out to $$y' = \frac {1} {4\sqrt{x}\sqrt{1+\sqrt{x}}}$$

But have no ideas on how to get there or where to start.

Answer 1

Do you know the chain rule? Usually when you have to take a derivative of something of the form $f(g(x))$, that's where you start. The chain rule says that the derivative is $$f'(g(x))\cdot g'(x).$$