Asked 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<sup>-x<sup>2</sup></sup> then
f'(x) = -2x*e<sup>-x<sup>2</sup></sup> = -2x*f(x)
f"(x) = (4x<sup>2</sup> - 2))e<sup>-x<sup>2</sup></sup> = f(x)*(4x<sup>2</sup> - 2))
f"'(x)= f'(x)*(4x<sup>2</sup> - 2)) + f(x)(8x) = -2x*f(x)*(4x<sup>2</sup> - 2)) =
f(x)(-8x<sup>3</sup> + 12x)
f""(x) = f'(x)*(-8x<sup>3</sup> + 12x) + f(x)(-24<sup>2</sup> + 12)=
-2x*f(x)(-8x<sup>3</sup> + 12x) + f(x)(-24<sup>2</sup> + 12) =
f(x)(16x<sup>4</sup>-48x + 12)
Be sure to verify my algebra.
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<sup>-x<sup>2</sup></sup> then
f'(x) = -2x*e<sup>-x<sup>2</sup></sup> = -2x*f(x)
f"(x) = (4x<sup>2</sup> - 2))e<sup>-x<sup>2</sup></sup> = f(x)*(4x<sup>2</sup> - 2))
f"'(x)= f'(x)*(4x<sup>2</sup> - 2)) + f(x)(8x) = -2x*f(x)*(4x<sup>2</sup> - 2)) =
f(x)(-8x<sup>3</sup> + 12x)
f""(x) = f'(x)*(-8x<sup>3</sup> + 12x) + f(x)(-24<sup>2</sup> + 12)=
-2x*f(x)(-8x<sup>3</sup> + 12x) + f(x)(-24<sup>2</sup> + 12) =
f(x)(16x<sup>4</sup>-48x + 12)
Be sure to verify my algebra.
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