How do you differentiate #f(x)= 7xsin2x# using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer Mia Oct 24, 2016 #f'(x)=7sinx+14xcos2x# Explanation: The product rule of derivatives is: #color(blue)((u(x)*v(x))'=u'(x)*v(x)+v'(x)*u(x))# #f'(x)=7(xsin2x)'# #f'(x)=7*(color(blue)(x'sinx+x(sin2x)'))# #f'(x)=7*(1*sinx+x(2cos2x)# #f'(x)=7*(sinx+2xcos2x)# #f'(x)=7sinx+14xcos2x# 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 1148 views around the world You can reuse this answer Creative Commons License