How do you differentiate #g(y) =(x^3 + x)(4x^2+5) # using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer Guilherme N. Jan 1, 2016 Product rule states that for #y=f(x)g(x)#, then #y'=f'(x)g(x)+f(x)g'(x)# Explanation: #(dy)/(dx)=(3x^2+1)(4x^2+5)+(x^3+x)(8x)# #(dy)/(dx)=(12x^4+15x^2+4x^2+5)+(8x^4+8x^2)# #(dy)/(dx)=20x^4+27x^2+5# 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 1573 views around the world You can reuse this answer Creative Commons License