How do you differentiate #f(x)=(x^2+sinx)(x-cosx)# using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer Ayush S. May 13, 2018 #=3x^2-xcosx+(1+x^2)sinx-cos2x# Explanation: #f(x)=(x^2+sinx)(x−cosx)# #f^'(x)=(x^2+sinx)d/dx(x−cosx)+(x−cosx)d/dx(x^2+sinx)# #=(x^2+sinx)(1+sinx)+(x−cosx)(2x+cosx)# #=x^2+sinx+x^2sinx+sin^2x+2x^2-2xcosx+xcosx-cos^2x# #=sin^2x-cos^2x+sinx(1+x^2)-xcosx+3x^2# #=3x^2-xcosx+(1+x^2)sinx-cos2x# 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 1558 views around the world You can reuse this answer Creative Commons License