How do you differentiate #f(x)=lnx * sin4x# using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer Hoat V. Mar 11, 2018 #(sin4x)/x + 4lnxcos4x# Explanation: # (lnx)'(sin4x) + (sin4x)'lnx# #=(lnx) = 1/x# #=(sin4x)' = (cos4x)(4x)' = 4cos4x# #=1/x sin4x + 4cos4xlnx# #=(sin4x)/x + 4 lnx cos4x# 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 1658 views around the world You can reuse this answer Creative Commons License