How do you differentiate #f(x)= e^(3x) * (5x^2-x+1)^12# using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer Bdub Mar 10, 2016 #f'(x)=12e^(3x)(10x-1)(5x^2-x+1)^11+3e^(3x)(5x^2-x+1)^12# Explanation: #f=e^(3x), g=(5x^2-x+1)^12# #f'=e^(3x) * 3=3e^(3x), g'=12(5x^2-x+1)^11 *(10x-1)# #f'(x)=fg'+gf'# #f'(x)=12e^(3x)(10x-1)(5x^2-x+1)^11+3e^(3x)(5x^2-x+1)^12# 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 1229 views around the world You can reuse this answer Creative Commons License