Consider the following. 7 x + 7 y = 6 (a) Find y' by implicit differentiation. y' = Correct: Your answer is correct. (b) Solve the equation explicitly for y and differentiate to get y' in terms of x. y' = (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 with Step-by-step explanation:We are given that an equation [tex7x+7y=6[/tex]a.We have to find y' by implicit differentiation.Implicit function:That function which is consist of x and y.The value of y does not depend  x directly.Differentiate w.r.t x[tex]7+7\frac{dy}{dx}=0[/tex][tex]7\frac{dy}{dx}=-7[/tex][tex]\frac{dy}{dx}=\frac{-7}{7}=-1[/tex][tex]\frac{dy}{dx}=y'=-1[/tex]b.We have to solve the equation explicitly for y and differentiate to get y' in terms of x.Explicit function:It is that function in which y is directly depend  on x.[tex]7x+7y=6[/tex][tex]7y=6-7x[/tex][tex]y=\frac{6-7x}{7}[/tex]Differentiate w.r.t x[tex]y'=\frac{1}{7}(0-7)=-1[/tex][tex]y'=-1[/tex]c.We have to find solutions of part a and part b are consistent by substituting the expression of y into the solution of part a.When substitute [tex]y=\frac{6-7x}{7}[/tex]  in y' of part a.Then,[tex]y'=-1[/tex]Hence, solution of part a  and part b are consistent.