Note:- 1) If y = sqrt(nx) ; then dy/dx = n/[2*sqrt(nx)]

Now,

y = sqrt{2 - (e^x)}

Let g(x) = sqrt(x) ..............(outer function)

and f(x) = {2 - (e^x)}........(inner function)

Thus, g(f(x)) = sqrt{2 - (e^x)}

Now, dy/dx = y' = [1/2*sqrt{2 - (e^x)}]*[-e^(x)]

or, dy/dx = -(e^x)/[{2*sqrt{2 - (e^x)}}]

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