Consider the following.3x + 3y = 8(a) Find y' by implicit differentiation.(b) Solve the equation explicitly for y and differentiate to get y' in terms of x.(c) Check that your solutions to part (a) and (b) are consistent by substituting the expression for y into your solution for part (a).y' =

Answer:a.y'=-1b.y'=-1c.YesStep-by-step explanation:We are given that consider a function[tex]3x+3y=8[/tex]Implicit function: That function is a relation in which dependent variable can not be expressed in terms of independent variable Explicit function: It is that function in which dependent variable can be expressed in terms of independent variable.a.[tex]3x+3y=8[/tex]Differentiate w.r.t x then we get [tex]3+3\frac{dy}{dx}=0[/tex][tex]3\frac{dy}{dx}=-3[/tex][tex]\frac{dy}[dx}=\frac{-3}{3}=-1[/tex][tex]\frac{dy}{dx}=y'=-1[/tex]b.[tex]3x+3y=8[/tex][tex]3y=8-3x[/tex][tex]y=\frac{8-3x}{3}[/tex]Differentiate w.r.t x then we get[tex]\frac{dy}{dx}=\frac{-3}{3}=-1[/tex][tex]\frac{dy}{dx}=y'=-1[/tex]When we substituting the value of y obtained from part b into a solution of part a then we get [tex]y'=-1[/tex]Hence, solutions are consistent.