What is the second derivative of #x^2sinx#? Calculus Basic Differentiation Rules Product Rule 1 Answer 1s2s2p Apr 25, 2018 #(d^2y)/(dx^2)=2sinx+4xcosx-x^2sinx# Explanation: We have #y=x^2sinx# #dy/dx=d/dx[x^2]sinx+x^2d/dx[sinx]=2xsinx+x^2cosx# #(d^2y)/(dx^2)=d/dx[2x]sinx+2xd/dx[sinx]+d/dx[x^2]cosx+x^2d/dx[cosx]=2sinx+2xcosx+2xcosx-x^2sinx=2sinx+4xcosx-x^2sinx# Answer link Related questions What is the Product Rule for derivatives? How do you apply the product rule repeatedly to find the derivative of #f(x) = (x - 3)(2 - 3x)(5 - x)# ? How do you use the product rule to find the derivative of #y=x^2*sin(x)# ? How do you use the product rule to differentiate #y=cos(x)*sin(x)# ? How do you apply the product rule repeatedly to find the derivative of #f(x) = (x^4 +x)*e^x*tan(x)# ? How do you use the product rule to find the derivative of #y=(x^3+2x)*e^x# ? How do you use the product rule to find the derivative of #y=sqrt(x)*cos(x)# ? How do you use the product rule to find the derivative of #y=(1/x^2-3/x^4)*(x+5x^3)# ? How do you use the product rule to find the derivative of #y=sqrt(x)*e^x# ? How do you use the product rule to find the derivative of #y=x*ln(x)# ? See all questions in Product Rule Impact of this question 6136 views around the world You can reuse this answer Creative Commons License