If f(x)=e^squ root of x ln squ root of x, find F'(x)

If your function is f(x) = e^sqrt[x*ln(sqrt x)], then it's
first derivative will be calculated using the chain rule and the product
rule.

f'(x) = e^sqrt[x*ln(sqrt x)]*[x*ln(sqrt
x)]'/2*sqrt[x*ln(sqrt x)]

f'(x) = e^sqrt[x*ln(sqrt
x)]*[x'*ln(sqrt x) + x*[ln(sqrt x)]']'/2*sqrt[x*ln(sqrt
x)]

f'(x) = e^sqrt[x*ln(sqrt x)]*[ln(sqrt x) +
x/2x)]/2*sqrt[x*ln(sqrt x)]

f'(x) = e^sqrt[x*ln(sqrt
x)]*[ln(sqrt x) + 1/2)]/2*sqrt[x*ln(sqrt x)]

The requested
1st derivative of the function is:

f'(x) =
{e^sqrt[x*ln(sqrt x)]}*[ln(sqrt x) + 1/2)]/2*sqrt[x*ln(sqrt
x)]