What is the fourth derivative of

Question

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.