How do you differentiate #f(x)=(x^2+4x)*(x^3+2x+1)# using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer Guilherme N. Dec 31, 2015 Product rule states that for #y=f(x)g(x)#, then #(dy)/(dx)=f'(x)g(x)+f(x)g'(x)#. Explanation: #(dy)/(dx)=(2x+4)(x^3+2x+1)+(x^2+4x)(3x^2+2)# #(dy)/(dx)=(2x^4+4x^3+4x^2+10x+4)+(3x^4+12x^3+2x^2+8x)# #(dy)/(dx)=5x^4+16x^3+6x^2+18x+4# 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 1598 views around the world You can reuse this answer Creative Commons License