You could use the product rule:

assuming that f(x) = a(x)·b(x)

then f'(x) = a(x)·b'(x) + b(x)·a'(x)

For the problem f(x) = x·e^{x}, let a(x) = c and b(x) = e^{x}, (which makes a'(x) = 0 and b'(x) = e^{x})

then f'(x) = c·e^{x} + e^{x}·0

so f'(x) = c·e^{x}