How do you differentiate #f(x)=(5e^x+cosx)(x-2)# using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer Gerardina C. Feb 10, 2017 #=5xe^x-5e^x-xsinx+2sinx+cosx# Explanation: If #f(x)=g(x)*h(x)#, you know that #f'(x)=g'(x)*h(x)+g(x)*h'(x)# (product rule), then #f'(x)=(5e^x-sinx)(x-2)+(5e^x+cosx)*1# #=5xe^x-xsinx-10e^x+2sinx+5e^x+cosx# #=5xe^x-5e^x-xsinx+2sinx+cosx# 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 1675 views around the world You can reuse this answer Creative Commons License