The first derivative is e^(2x)[1+2x] and the second is 4e^(2x)[x+1]
As far as my knowledge is concerned, The derivative can be calculated by
using d/dx(uv) = u dv/dx + v du/dx
d/dx(xe^2x) = x d/dx(e^2x) + e^2x as d/dx x = 1
= 2x e^2x + e^2x as d/dx(e^y) = e^y dy/dx [using chain rule]
Therefore, the derivative of xe^(2x)=1.
Hope this is useful.
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