What is the derivative of # f(x) = 3x^2 ln 2x#? Calculus Basic Differentiation Rules Product Rule 1 Answer Andrea S. Nov 4, 2017 #d/dx ( 3x^2ln2x) = 3x( 1+ 2ln 2x )# Explanation: Using the product rule: #d/dx ( 3x^2ln2x) = d/dx(3x^2)ln 2x + 3x^2 d/dx (ln2x)# #d/dx ( 3x^2ln2x) = 6xln 2x + 3x^2 2/(2x)# #d/dx ( 3x^2ln2x) = 6xln 2x + 3x# #d/dx ( 3x^2ln2x) = 3x( 1+ 2ln 2x )# 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 4205 views around the world You can reuse this answer Creative Commons License