How do you differentiate #f(x)=-xe^x*(4-x)/6# using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer 1s2s2p Mar 20, 2018 #f'(x)=(xe^x)/6-(xe^x(4-x))/6-(e^x(4-x))/6# Explanation: If a function #f(x)=uvw# where #u#, #v# and #w# are all functions of #x#, then #f'(x)=uvw'+uv'w+u'vw# #u=-x# #u'=-1# #v=e^x# #v'=e^x# #w=(4-x)/6=4/6-x/6# #w'=-1/6# #f'(x)=(xe^x)/6-(xe^x(4-x))/6-(e^x(4-x))/6# 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 1516 views around the world You can reuse this answer Creative Commons License