How do you differentiate #f(x)=(e^x+x)(cotx+x)# using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer Maharshi Mar 5, 2016 # [(e^x +1) * (cot x + x)] + [ (e^x +x) * (1 - csc^2x)]# Explanation: #d/dx e^x = e^x# #d/dx x = 1# #d/dx cot x = -csc^2x# #d/dx x = 1# According to product rule, #f'(x) = [d/dx e^x + d/dx x] * (cot x + x) + (e^x +x) * [d/dx cot x + d/dx x]# #= [(e^x +1) * (cot x + x)] + [ (e^x +x) * (1 - csc^2x)]# 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 1665 views around the world You can reuse this answer Creative Commons License