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.
