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