How do you derive #y = (4x^4 − 2) / (-x^2 + 1)# using the quotient rule? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Lucy Apr 9, 2018 #(dy)/(dx)=(16x^3-8x^5-4x)/(-x^2+1)^2# Explanation: #y=(4x^4-2)/(-x^2+1)# #(dy)/(dx)=((-x^2+1)(16x^3)-(4x^4-2)(-2x))/(-x^2+1)^2# #(dy)/(dx)=(-16x^5+16x^3+8x^5-4x)/(-x^2+1)^2# #(dy)/(dx)=(16x^3-8x^5-4x)/(-x^2+1)^2# Answer link Related questions What is the Quotient Rule for derivatives? How do I use the quotient rule to find the derivative? How do you prove the quotient rule? How do you use the quotient rule to differentiate #y=(2x^4-3x)/(4x-1)#? How do you use the quotient rule to differentiate #y=cos(x)/ln(x)#? How do you use the quotient rule to find the derivative of #y=tan(x)# ? How do you use the quotient rule to find the derivative of #y=x/(x^2+1)# ? How do you use the quotient rule to find the derivative of #y=(e^x+1)/(e^x-1)# ? How do you use the quotient rule to find the derivative of #y=(x-sqrt(x))/(x^(1/3))# ? How do you use the quotient rule to find the derivative of #y=x/(3+e^x)# ? See all questions in Quotient Rule Impact of this question 1412 views around the world You can reuse this answer Creative Commons License