Question #aef8a Calculus Basic Differentiation Rules Product Rule 1 Answer marfre Mar 27, 2017 #y^((4)) = 24x^-5 = 24/x^5# Explanation: Find the Fourth derivative: #y = 2x^2 + x-1 + 1/x = 2x^2 + x-1 + x^(-1)# #y' = 4x + 1 -x^(-2) = 4x + 1 -1/x^2# #y'' = 4 +2x^-3 = 4+2/x^3# #y''' = -6x^-4 = -6/x^4# #y^((4)) = 24x^-5 = 24/x^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 1184 views around the world You can reuse this answer Creative Commons License