请问f(x)=(1/根号下2π)·e^(-x^2/2)的一阶导和二阶导是什么呢?

Question

请问f(x)=(1/根号下2π)·e^(-x^2/2)的一阶导和二阶导是什么呢?

Answer 1

f(x)=(1/√2π)*e^(-x^2/2)
一阶导：
f(x)'=(1/√2π)*e^(-x^2/2)*(-x^2/2)*(-2x/2)=(-1/2√2π)*(x^3)*e^(-x^2/2)
二阶导：
f(x)“=(-3/2√2π)*(x^2)*e^(-x^2/2)+(-1/2√2π)*(x^3)*e^(-x^2/2)*(-x^2/2)*(-2x/2)
=(-3/2√2π)*(x^2)*e^(-x^2/2)+(-1/4√2π)*(x^6)*e^(-x^2/2)
=(-1/2√2π)*(x^2)*e^(-x^2/2)(3+1/2x^4)