How do you differentiate #f(x)=xe^(3x)# using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer sjc Jan 10, 2017 #f'(x)=e^(3x)(1+3x)# Explanation: The product rule for differentiation is: #f(x)=uv,# where #u# & #v# are both functions of #x# #f'(x)=vu'+uv'# #f(x)=xe^(3x)# #u=x=>u'=1# #v=e^(3x)=>v'=3e^(3x)# #:.f'(x)=e^(3x)xx1+x xx3e^(3x)# #f'(x)=e^(3x)+3xe^(3x)# #f'(x)=e^(3x)(1+3x)# 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 7875 views around the world You can reuse this answer Creative Commons License