Question

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 1

a.y'=-1

b.y'=-1

c.Yes

Explanation:

We are given that consider a function

`3x+3y=8`

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.
`3x+3y=8`

Differentiate w.r.t x then we get

`3+3(dy)/(dx)=0`

`3(dy)/(dx)=-3`

`\frac{dy}[dx}=(-3)/(3)=-1`

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

b.
`3x+3y=8`

`3y=8-3x`

`y=(8-3x)/(3)`

Differentiate w.r.t x then we get

`(dy)/(dx)=(-3)/(3)=-1`

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

When we substituting the value of y obtained from part b into a solution of part a then we get

`y'=-1`

Hence, solutions are consistent.