How do you differentiate #f(x)=(2e^x+sinx)(x-2)# using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer ali ergin Mar 7, 2016 #d/(d x) f(x)=(x-2)(2e^x+cos x)+sin x# Explanation: #f(x)=(2e^x+sin x)(x-2)# #d/(d x) f(x)=d/(d x)(2e^x+sin x)(x-2)+d/(d x)(x-2)(2e^x+sin x)# #d/(d x) f(x)=(2e^x+cos x)(x-2)+(2e^x+sin x)# #d/(d x) f(x)=2xe^x+x cos x-4e^x-2cos x+2e^x+sin x# #d/(d x) f(x)=2xe^x-2e^x+x cos x-2cos x+sin x# #d/(d x) f(x)=2e^x(x-2)+cos x(x-2)+sin x# #d/(d x) f(x)=(x-2)(2e^x+cos x)+sin x# 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 1348 views around the world You can reuse this answer Creative Commons License