What is the derivative of #f(x)=( e^(2x))(Ln(x^2+1))#? Calculus Basic Differentiation Rules Product Rule 1 Answer F. Javier B. May 23, 2018 See process below Explanation: We know that #(h·g)´(x)=color(red)h´·color(blue)g+color(green)h·g´# Then in our case #f´(x)=color(red)(2e^(2x))color(blue)(ln(x^2+1))+color(green)(e^(2x))(2x)/(x^2+1)=# #=2e^(2x)(ln(x^2+1)+x/(x^2+1))# 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 3094 views around the world You can reuse this answer Creative Commons License