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"If "x^(3)+y^(3)=3 axy," find "(dy)/(dx)...

`"If "x^(3)+y^(3)=3 axy," find "(dy)/(dx).`

Text Solution

Verified by Experts

The correct Answer is:
`(ay-x^(2))/(y^(2)-ax)`
Given `x^(3)+y^(3)-3axy = 0`. From
`(dy)/(dx)=-("differentiating f w.r.t. x keeping y as consant")/("differentiating f w.r.t. y keeping x as constant")`
`=-(3x^(2)-3ay)/(3y^(2)-3ax)=(ay-x^(2))/(y^(2)-ax)`
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