How do you differentiate #f(x)=(5e^x+tanx)(x^2-2x)# using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer 1s2s2p Apr 25, 2018 #f'(x)=(5e^x+sec^2x)(x^2-2x)+(5e^x+tanx)(2x-2)# Explanation: For #f(x)=(5e^x+tanx)(x^2-2x)#, we find #f'(x)# by doing: #f'(x)=d/dx[5e^x+tanx] (x^2-2x)+(5e^x+tanx)d/dx[x^2-2x]# #f'(x)=(5e^x+sec^2x)(x^2-2x)+(5e^x+tanx)(2x-2)# 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 1438 views around the world You can reuse this answer Creative Commons License