How do you find #(df)/dy# and #(df)/dx# of #f(x,y)=(4x-2y)/(4x+2y)#, using the quotient rule? Calculus Basic Differentiation Rules Quotient Rule 1 Answer VinÃcius Ferraz Nov 30, 2015 #f_x (x,y) = (4y)/((2x + y)^2)# #f_y (x,y) = (-4x)/((2x+y)^2)# Explanation: #f(x, y) = (2x - y)/(2x + y) = u/v# #(partial f)/(partial x) = f_x = frac{u_x v - u v_x}{v^2} = frac{2(2x+y) - (2x-y)*2}{(2x + y)^2}# #(partial f)/(partial y) = f_y = frac{u_y v - u v_y}{v^2} = frac{-1(2x+y) - (2x-y)*1}{(2x + y)^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 510 views around the world You can reuse this answer Creative Commons License