Question

Find dy/dx by implicit differentiation. x2 − 8xy + y2 = 8

Answer 1

`(dy)/(dx) = (8y - 2x)/(2y - 8x)`

Explanation:

The denominator is always the variable that we want to find the derivation in relation of. So it is always dx.

The number is the variable we derivated. So

`x^(2) - 8xy + y^(2) = 8`

`2x(dx)/(dx) - 8y(dx)/(dx) - 8x(dy)/(dx) + 2y(dy)/(dx) = 0`

`2x - 8y + (2y - 8x)(dy)/(dx) = 0`

`(2y - 8x)(dy)/(dx) = 8y - 2x`

`(dy)/(dx) = (8y - 2x)/(2y - 8x)`

Answer 2

we have that

x² − 8xy + y² = 8
2x-8y-8x(dy/dx)+2y*(dy/dx)=0
8x(dy/dx)-2y*(dy/dx)=2x-8y
[8x-2y]*(dy/dx)=2x-8y
(dy/dx)=[2x-8y]/[8x-2y]
(dy/dx)=2*[x-4y]/2*[4x-y]
(dy/dx)=[x-4y]/[4x-y]

the answer is
(dy/dx)=[x-4y]/[4x-y]