How do you find derivative of #f(x)=(x^2+4x+3)/(sqrtx)#? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Massimiliano Apr 20, 2015 In this way: #y'=((2x+4)*sqrtx-(x^2+4x+3)*1/(2sqrtx))/(sqrtx)^2=# #=(((2x+4)sqrtx*2sqrtx-x^2-4x-3)/(2sqrtx))/x=# #=((2x+4)*2x-x^2-4x-3)/(2xsqrtx)=# #=(4x^2+8x-x^2-4x-3)/(2xsqrtx)=(3x^2+4x-3)/(2xsqrtx)#. 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 7509 views around the world You can reuse this answer Creative Commons License