How do you differentiate #f(x) = ( 4x - 3) ( xe^x)# using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer Leland Adriano Alejandro Jan 12, 2016 #f' (x)=e^x*(4x^2+5x-3)# Explanation: from the given f(x)=(4x-3)(x*e^x)# #f' (x)=(4x-3)(1*e^x+x*e^x)+x*e^x*4# #f' (x)=e^x*(1+x)(4x-3)+4x*e^x# #f' (x)=e^x((x+1)(4x-3)+4x)# #f' (x)=e^x(4x^2+x-3+4x)# #f' (x)=e^x(4x^2+5x-3)# 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 1558 views around the world You can reuse this answer Creative Commons License