Question

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 1

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

`7+7(dy)/(dx)=0`

`7(dy)/(dx)=-7`

`(dy)/(dx)=(-7)/(7)=-1`

`(dy)/(dx)=y'=-1`

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.

`7x+7y=6`

`7y=6-7x`

`y=(6-7x)/(7)`

Differentiate w.r.t x

`y'=(1)/(7)(0-7)=-1`

`y'=-1`

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
`y=(6-7x)/(7)` in y' of part a.

Then,
`y'=-1`

Hence, solution of part a and part b are consistent.