Derivatives
posted by 413 .
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.
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