How do you find the derivative of # f(x) = 3xsin(2x)^2#? Calculus Basic Differentiation Rules Product Rule 1 Answer Shwetank Mauria May 24, 2016 #(df(x))/(dx)=3sin(2x)^2+24x^2cos(2x)^2# Explanation: To find the derivative of #f(x)=3xsin(2x)^2#, we use poduct formula and chain rule. #(df(x))/(dx)=1xx3sin(2x)^2+3x xxcos(2x)^2xx8x# = #3sin(2x)^2+24x^2cos(2x)^2# 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 1437 views around the world You can reuse this answer Creative Commons License