How do you derive #y = (x^2+8x+3)/x^(1/2)# using the quotient rule? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Hoat V. Mar 11, 2018 #(3x^2 + 8x - 3)/(2x^(3/2))# Explanation: #=[(x^2 + 8x + 3)'(x^(1/2)) - (x^(1/2))'(x^2 +8x + 3)]/(x^(1/2))^2# #=[x^(1/2)(2x+8) - 1/2x^(-1/2)(x^2+8x+3)]/x# #=[2x^(3/2) + 8x^(1/2) - 1/2x^(3/2) - 4x^(1/2) - 3/2x^(-1/2)]/x# #=[3/2x^(3/2) + 4x^(1/2)-3/2x^(-1/2)]/x# #=[x^(-1/2)[3/2x^2 + 4x -3/2]]/x# #=[(3x^2 + 8x + 3)/2]/x^(3/2)# #=(3x^2 + 8x + 3)/(2x^(3/2))# 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 1215 views around the world You can reuse this answer Creative Commons License