Question #7454e Calculus Graphing with the Second Derivative Notation for the Second Derivative 1 Answer Andrea S. Jul 19, 2017 #d^2/dx^2 (x^3logx) = x(6logx + 5)# Explanation: Using the product rule for the second order derivative: #d^2/dx^2 (x^3logx) = (d^2/dx^2 x^3)logx +2 (d/dx x^3)(d/dx logx) + x^3(d^2/dx^2 logx)# #d^2/dx^2 (x^3logx) = 6xlogx +2 xx 3x^2 xx 1/x + x^3(-1/x^2)# #d^2/dx^2 (x^3logx) = 6xlogx +6x -x# #d^2/dx^2 (x^3logx) = 6xlogx + 5x# #d^2/dx^2 (x^3logx) = x(6logx + 5)# Answer link Related questions What is notation for the Second Derivative? What is Leibniz notation for the second derivative? What is the second derivative of #e^(2x)#? How do you find the first, second derivative for #3x^(2/3)-x^2#? What is the second derivative of #y=x*sqrt(16-x^2)#? How do you find the first and second derivative of #(lnx)/x^2#? How do you find the first and second derivative of #lnx^(1/2)#? How do you find the first and second derivative of #x(lnx)^2#? How do you find the first and second derivative of #ln(x^2-4)#? How do you find the first and second derivative of #ln(lnx^2)#? See all questions in Notation for the Second Derivative Impact of this question 1625 views around the world You can reuse this answer Creative Commons License