How do you find the derivative of #e^((x^2)/2)#? Calculus Basic Differentiation Rules Chain Rule 1 Answer NJ Mar 14, 2018 #f'(x) = xe^(x^2/2)# Explanation: #f(x) = e^(x^2/2)# We need to use the chain rule: #f'(x) = (d(e^(x^2/2)))/(d(x^2/2)) * (d(x^2/2))/(dx)# #f'(x) = e^(x^2/2) * ((2x)/2)# #f'(x) = xe^(x^2/2)# Answer link Related questions What is the Chain Rule for derivatives? How do you find the derivative of #y= 6cos(x^2)# ? How do you find the derivative of #y=6 cos(x^3+3)# ? How do you find the derivative of #y=e^(x^2)# ? How do you find the derivative of #y=ln(sin(x))# ? How do you find the derivative of #y=ln(e^x+3)# ? How do you find the derivative of #y=tan(5x)# ? How do you find the derivative of #y= (4x-x^2)^10# ? How do you find the derivative of #y= (x^2+3x+5)^(1/4)# ? How do you find the derivative of #y= ((1+x)/(1-x))^3# ? See all questions in Chain Rule Impact of this question 1370 views around the world You can reuse this answer Creative Commons License