y=(x^2-2x+3)*e^(-x^2) 求导数

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y=(x^2-2x+3)*e^(-x^2) 求导数
y=(x^2-2x+3)*e^(-x^2) 求导数

y=(x^2-2x+3)*e^(-x^2) 求导数
y'=(x^2-2x+3)'*e^(-x^2)+(x^2-2x+3)*[e^(-x^2)]'
=(2x-2)*e^(-x^2)+(x^2-2x+3)*e^(-x^2)*(-x^2)'
=(2x-2)*e^(-x^2)-2x(x^2-2x+3)*e^(-x^2)
=(2x-2)*e^(-x^2)-(2x^3-4x^2+6x)*e^(-x^2)
=(2x-2-2x^3+4x^2-6x)*e^(-x^2)
=(-2x^3+4x^2-4x)*e^(-x^2)

y=(x^2-2x+3)*e^(-x^2)
y'=(x^2-2x+3)'*e^(-x^2)+(x^2-2x+3)*[e^(-x^2)]'
=(2x-2)*e^(-x^2)+(x^2-2x+3)*e^(-x^2)*(-x^2)'
=e^(-x^2)*[2x-2+(x^2-2x+3)*(-2x)]
=e^(-x^2)*[(2x-2-2x^3+4x^2-6x)]
=e^(-x^2)*(-2x^3+4x^2-4x-2)