calculus question

f(x) = x^2 e^-x - 2x e^x + d/dx (x^2 e^x)
g(x) = sin(√x)

(a) what are the largest possible domains of f and g, respectively?
(b) determine, with reason(s), whether the functions f and g are even, odd, or neither.
(c) determine whether the functions f and g are periodic. state the period of the function if it is periodic.
(d) let h = g o f, ie, y = h(x) if and only if y = g( f(x)). find the largest possible domain of h, whether h is even or odd, whether h is periodic and its period if appropriate.
(e) find the derivative h'(x) at x = 1. (do not try to find h'(x) for every x.)

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need steps and explanation briefly. thanks!!!