How do you find the first and second derivative of #x^2 lnx#? Calculus Graphing with the Second Derivative Notation for the Second Derivative 1 Answer ali ergin Aug 31, 2016 #(d y)/(d x)=2x*l n(x)+x" 'The first derivative '"# #(d^2y)/(d x^2)=2*l n(x)+3" 'The second derivative '"# Explanation: #y=x^2* l n (x)# #u=x^2" ; " u'=2x# #v=l n (x)" ; "v^'=1/x# #y=u*v# #(d y)/(d x)=u^'*v+v^'*u# #(d y)/(d x)=2x* l n(x)+1/cancel(x)*cancel(x)^2# #(d y)/(d x)=2x*l n(x)+x" 'The first derivative '"# #a=2x" ; "a^'=2# #b=l n(x)" ; "b^'=1/x# #(d^2y)/(d x^2)=a^'*b+b^'*a+1# #(d^2y)/(d x^2)=2*l n(x)+1/cancel(x)*2cancel(x)+1# #(d^2y)/(d x^2)=2*l n(x)+2+1# #(d^2y)/(d x^2)=2*l n(x)+3" 'The second derivative '"# 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 1720 views around the world You can reuse this answer Creative Commons License