SOLUTION: Find dy/dx by implicit differentiation, where 4x^6+3x^4y-4xy^6=6. dy/dx=?

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Question 1160312: Find dy/dx by implicit differentiation, where 4x^6+3x^4y-4xy^6=6.
dy/dx=?
Found 2 solutions by solver91311, ikleyn:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Did you mean but forgot to hold the Shift key or did you mean but hit the key one to the right of the one you intended? Not that it matters much, but you need to learn to proofread your post BEFORE you submit.


John

My calculator said it, I believe it, that settles it

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

I will do it, but I will use more compact designation  " y' "  for the derivative %28dy%29%2F%28dx%29.



    24x^5 + (12x^3y + 3x^4*y') - 4y^6 -24xy^5*y' = 0


Now re-group the terms, collecting the terms with  " y' " in one group


    24x^5 + 12x^3y - 4y^6 = (-3x^4 + 24y^5)*y'


Now express  y'


    y' = %2824x%5E5+%2B+12x%5E3y+-+4y%5E6%29%2F%28-3x%5E4+%2B+24y%5E5%29.


It is your answer.

Solved.