$\text{ If the functions }\mathrm{f}\left(\mathrm{x}\right)\text{ and }\mathrm{\varphi }\left(\mathrm{x}\right)\text{ are continuous in }[\mathrm{a},\mathrm{b}]\text{ and differentiable in }(\mathrm{a},\mathrm{b})\text{, then }$$\text{ the value of ' }{\mathrm{c}}^{\mathrm{\prime }}\text{ for the pair of functions }\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{x}},\mathrm{\varphi }\left(\mathrm{x}\right)=\frac{1}{\sqrt{\mathrm{x}}}\text{ is }$