How do you implicitly differentiate $-y=xy+2sqrt(x-y^3)$ ?

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Answer 1 · 2017-08-18T13:40:29

$dy/dx=-(x-y^3)^(1/2)/(x(x-y^3)^(1/2)+(1-3y^2)+(x-y^3)^(1/2)$

$-dy/dx$ $=xdy/dx+y+$ ...

$2sqrt(x+y^3)=$ $2(x-y^3)^(1/2)$ derivative of that equal to

$(x-y^3)^(-1/2)*(1-3y^2dy/dx)$

with some math

get $dy/dx$ in one side and all in the other side

$dy/dx=-(x-y^3)^(1/2)/(x(x-y^3)^(1/2)+(1-3y^2)+(x-y^3)^(1/2)$

I need someone to check my answer or explain further, and I will be thankful.

How do you implicitly differentiate -y=xy+2sqrt(x-y^3) -y=xy+2sqrt(x-y^3) ?