How do you find the derivative of #y = (x^2+4x+3)/x^.5#? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Jim H Jul 11, 2015 If this is #y = (x^2+4x+3)/x^0.5#, we can use the quotient rule or rewrite as follows. Explanation: #y = (x^2+4x+3)/x^0.5 = x^2/x^0.5 +(4x)/x^0.5+3/x^0.5# # = x^1.5 +4x^0.5 +3x^-0.5# So #y' = 1.5x^0.5 +2x^-0.5 +1.5 x^-1.5# 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 1738 views around the world You can reuse this answer Creative Commons License