How do you differentiate #f(x)=(x+1)/sqrtx# using the quotient rule? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Monzur R. Apr 6, 2018 #f'(x)=(x-1)/(xsqrtx)# Explanation: Let #f(x)=(x+1)/sqrtx#. To find #f'#, we will use the quotient rule #d/dxu/v=(vu'-uv')/v^2# So #f'(x)=d/dx(x+1)/sqrtx=(sqrtxd/dx(x+1)-(x+1)d/dxsqrtx)/(sqrtx)^2=(sqrtx-(x+1)/(2sqrtx))/x=(2x-x-1)/(2xsqrtx)=(x-1)/(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 1361 views around the world You can reuse this answer Creative Commons License