Correct Answer - Option 1 :
\(\dfrac{xe^x}{ex^e}\)
Concept:
The differentiation of f(x) wrt g(x) = \(\rm f'(x)\over g'(x)\)
f(x) and g(x) be the function of x
Calculation:
f(x) = ex
f'(x) = \(\rm {d\over dx}e^x = e^x\)
g(x) = xe
g'(x) = \(\rm {d\over dx}x^e = ex^{e-1}\)
Required derivative D = \(\rm f'(x)\over g'(x)\)
D = \(\rm e^x\over ex^{e-1}\) = \(\rm xe^x\over ex^e\)