Implicit derivation, where is my mistake ?

Question

The starting equation is :

4x^2 - 2xy - 8x + y^2 + 2y = 5

I derivate as follow:

8x - 2y - 2xy' - 8 + 2yy' +2y' =0

y' ( -2x + 2y + 2 ) = -8x + 2y +8

y' = ( -8x + 2y +8 ) / ( -2x + 2y + 2 )

= ( y - 4x + 4 ) / ( y - x + 1 )

which I think is right, but my TI gives me this answer with ImpDif function :

( -4x + 4) / ( y + 1 )

Where is my mistake ????

Answer 1

You did it right. The calculator gave a wrong answer. It happens sometimes. Your mistake was to trust a calculator.

Answer 2

When you differentiate implicitly (not "derivate"), you get

8x - 2y - 2xy' - 8 + 2yy' + 2y' = 0

Isolate y':

8x-2y-8 = (2x - 2y + 2)y'

which gives

y' = (8x-2y-8) / (2x-2y+2)
= (4x-y-4) / (x-y+1)

which is equivalent to what you got. It seems as though your calculator did not properly handle the y^2 term. If it simply got 2y instead of 2yy', then it would cancel with the -2y, and got the answer that it reported.

Answer 3

i often snort and say im fantastic, yet im a perfectionist and that i take even a minor mistake noticeably difficult. if i shrink to rubble, say, at a karaoke, i'm going to on no account hear to that music back. whether i shrink to rubble at something and it isnt my fault, if somebody mentions it YEARS later i nonetheless get disenchanted. phsycologically undesirable, i understand, yet i come across it incredibly difficult to forgive myself.

Answer 4

Well,first of all you can`t derive byx ,then by.You have to choose the variable