What are the critical points of #f(x) =e^x-x^2e^(x^2)#? Calculus Graphing with the First Derivative Identifying Stationary Points (Critical Points) for a Function 1 Answer Lithia Jul 24, 2017 #f'(x) = e^x -2xe^(x^2) + e^x(2xe^(x^2))# Explanation: #(e^x)' = e^x# #(e^u)' = e^u*u'# #f(x) = e^x - x^2*e^(x^2)# use the Product Rule #f'g + fg'# for #x^2*e^(x^2)# #f'(x) = e^x - (2x)(e^(x^2))+(e^x)(2xe^(x^2))# #f'(x) = e^x -2xe^(x^2) + e^x(2xe^(x^2))# Answer link Related questions How do you find the stationary points of a curve? How do you find the stationary points of a function? How many stationary points can a cubic function have? How do you find the stationary points of the function #y=x^2+6x+1#? How do you find the stationary points of the function #y=cos(x)#? How do I find all the critical points of #f(x)=(x-1)^2#? Let #h(x) = e^(-x) + kx#, where #k# is any constant. For what value(s) of #k# does #h# have... How do you find the critical points for #f(x)=8x^3+2x^2-5x+3#? How do you find values of k for which there are no critical points if #h(x)=e^(-x)+kx# where k... How do you determine critical points for any polynomial? See all questions in Identifying Stationary Points (Critical Points) for a Function Impact of this question 1515 views around the world You can reuse this answer Creative Commons License