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If x^(4) + y^(4) = 3xy, "then " (dy)/(d...

If ` x^(4) + y^(4) = 3xy, "then " (dy)/(dx)` is equal to

A

`(4y^(3) -3x)/(4x^(3) - 3y)`

B

`(4x^(3) - 3y)/(4y^(3) 3x)`

C

`(3y -4x^(3))/(4y^(3) - 3x)`

D

`(4y^(3) - 3x)/(3y -4x^(3))`

Text Solution

Verified by Experts

The correct Answer is:
C
Given ` x^(4) + y^(4) = 3xy`
On differentiating both sides w.r.t.x we get
`4x^(3) + 4y^(3) (dy)/(dx) = 3 [ x(dy)/(dx) + y xx1]`
`rArr (dy)/(dx) (4y^(3) - 3x ) = 3y - 4x^(3)`
`rArr (dy)/(dx) = (3y - 4x^(3))/(4y^(3)-3x))`
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