Derivatives

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What is the fourth derivative of
f(x)= e^-x^2.

I got f''(x)=-2e^-x^2 + 4x^2e^-x^2

i need some help on find f''''(x)


You have
f(x) = e-x2 then
f'(x) = -2x*e-x2 = -2x*f(x)
f"(x) = (4x2 - 2))e-x2 = f(x)*(4x2 - 2))
f"'(x)= f'(x)*(4x2 - 2)) + f(x)(8x) = -2x*f(x)*(4x2 - 2)) =
f(x)(-8x3 + 12x)
f""(x) = f'(x)*(-8x3 + 12x) + f(x)(-242 + 12)=
-2x*f(x)(-8x3 + 12x) + f(x)(-242 + 12) =
f(x)(16x4-48x + 12)

Be sure to verify my algebra.

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