Posted by
**413** on
.

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) = (4x^{2} - 2))e^{-x2} = f(x)*(4x^{2} - 2))

f"'(x)= f'(x)*(4x^{2} - 2)) + f(x)(8x) = -2x*f(x)*(4x^{2} - 2)) =

f(x)(-8x^{3} + 12x)

f""(x) = f'(x)*(-8x^{3} + 12x) + f(x)(-24^{2} + 12)=

-2x*f(x)(-8x^{3} + 12x) + f(x)(-24^{2} + 12) =

f(x)(16x^{4}-48x + 12)

Be sure to verify my algebra.