How do you find the derivative for #f(x) = (2x+1)(4-x^2)(1+x^2)#? Calculus Basic Differentiation Rules Product Rule 1 Answer Massimiliano Jun 14, 2015 #y'=2(-5x^4-2x^3+9x^2-3x+4)#. Explanation: in this way: #y'=2*(4-x^2)(1+x^2)+(2x+1)* (-2x)*(1+x^2)+(2x+1)(4-x^2)*2x=# #=2(4+4x^2-x^2-x^4-2x^2-2x^4-x-x^3+8x^2-2x^4+4x-x^3)=# #=2(-5x^4-2x^3+9x^2-3x+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 2137 views around the world You can reuse this answer Creative Commons License