How do you differentiate #g(z) = z^2cos(z)e^(2+z)# using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer 1s2s2p May 10, 2018 #dy/dx=ze^(2+z)(zcos(z)-zsin(z)+2cos(z))# #dy/dx=ze^(2+z)((2+z)cos(z)-zsin(z))# Explanation: Given #y=uvw#, where #u, v# and #w# are all functions of #z#, then #y'=uvw'+uv'w+u'vw# #u=z^2# #u'=2x# #v=cos(z)# #v'=-sin(z)# #w=e^(2+z)# #w'=d/dz[2+z]e^(2+z)=e^(2+z)# So, #dy/dx=z^2cos(z)e^(2+z)-z^2sin(z)e^(2+z)+2zcos(z)e^(2+z)# #dy/dx=ze^(2+z)(zcos(z)-zsin(z)+2cos(z))# #dy/dx=ze^(2+z)((2+z)cos(z)-zsin(z))# 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 1607 views around the world You can reuse this answer Creative Commons License