How do you find the derivative and double derivative of the equation f(x)=xe^(-x^2)f(x)=xe−x2?
1 Answer
Aug 31, 2016
dy/dx=-2x^2e^(-x^2)+e^(-x^2)dydx=−2x2e−x2+e−x2
(d^2y)/(dx^2)=2xe^(-x^2)(2x^2-3x)d2ydx2=2xe−x2(2x2−3x)
Explanation:
Given -
y=xe^(-x^2)y=xe−x2
dy/dx=x.e^(-x^2)(-2x)+e^(-x^2)(1)dydx=x.e−x2(−2x)+e−x2(1)
dy/dx=-2x^2e^(-x^2)+e^(-x^2)dydx=−2x2e−x2+e−x2
(d^2y)/(dx^2)=[-2x^2.e^(-x^2)(-2x)+e^(-x^2)(-4x)]+[e^(-x^2)(-2x)]d2ydx2=[−2x2.e−x2(−2x)+e−x2(−4x)]+[e−x2(−2x)]
(d^2y)/(dx^2)=4x^3e^(-x^2)-4xe^(-x^2)-2xe^(-x^2)d2ydx2=4x3e−x2−4xe−x2−2xe−x2
(d^2y)/(dx^2)=4x^3e^(-x^2)-6xe^(-x^2)d2ydx2=4x3e−x2−6xe−x2
(d^2y)/(dx^2)=2xe^(-x^2)(2x^2-3x)d2ydx2=2xe−x2(2x2−3x)
