How do you differentiate #f(x)= (x^2+1)(5x^4+3^2+2x) # using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer sankarankalyanam May 7, 2018 Answer: #color(brown)(f'(x) = 30x^5 + 20x^3 + 6x^2 + 18x + 2# Explanation: #f(x) = (x^2 + 1) * (5x^4 + 2x + 3^2)# #Let " "u = ((x^2 + 1), v = (5x^4 + 2x + 9)# #(du)/(dx) = (d/(dx)) (x^2 + 1) = 2x# #(dv) / (dx) = d/(dx) (5x^4 + 2x + 9) = 20x^3 + 2# #f'(x) = v (du)/(dx) + u (dv)/(dx)# #f'(x) = (5x^4 + 2x + 9) * 2x + (x^2 + 1) * (20x^3 + 2)# #=> 10x^5 + 4x^2 + 18x + 20x^5 + 2x^2 + 20x^3 + 2# #color(brown)(=> 30x^5 + 20x^3 + 6x^2 + 18x + 2# 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 - ... 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 715 views around the world You can reuse this answer Creative Commons License