How do you differentiate #f(x)=(x^2 + 2) (x^3 + 4)# using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer mizoo Apr 28, 2018 #f'(x) = 5x^4 + 6x^2 + 8x # Explanation: #f'(x) = 2x xx (x^3 + 4) + 3x^2 xx (x^2 + 2)# #f'(x) = 2x^4 + 8x + 3x^4 + 6x^2 # #f'(x) = 5x^4 + 6x^2 + 8x # 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 1426 views around the world You can reuse this answer Creative Commons License