$\displaystyle \displaystyle \frac{\sqrt{2(x+h)-1)}-\sqrt{2x-1}}{h}$

$\displaystyle \displaystyle \frac{1}{h}(\sqrt{2(x+h)-1)}-\sqrt{2x-1})$

$\displaystyle \displaystyle \frac{1}{h}(\sqrt{2(x+h)-1)}-\sqrt{2x-1})\times \frac{\sqrt{2(x+h)-1)}+\sqrt{2x-1}}{\sqrt{2(x+h)-1)}+\sqrt{2x-1}}$

$\displaystyle \displaystyle \frac{1}{h}(\sqrt{2(x+h)-1)}-\sqrt{2x-1})\times \frac{\sqrt{2(x+h)-1)}+\sqrt{2x-1}}{\sqrt{2(x+h)-1)}+\sqrt{2x-1}}$

$\displaystyle \displaystyle \frac{1}{h}\left(\frac{2x+2h-1-2x+1}{\sqrt{2(x+h)-1)}+\sqrt{2x-1}}\right)$

$\displaystyle \displaystyle \frac{1}{h}\left(\frac{2h}{\sqrt{2(x+h)-1)}+\sqrt{2x-1}}\right)$

$\displaystyle \displaystyle \frac{2}{\sqrt{2(x+h)-1)}+\sqrt{2x-1}}$

Now

$\displaystyle \displaystyle h\to 0$