Question

find dy/dx of x^2y^2+xsin(y)=1 by implicit differentiation

Answer 1

\[(x^22yy'+2xy^2)+(xcosy(y')+siny(1))=0 => x^22yy'+2xy^2+xcosyy'+siny=0 => y'(x^22y+xcosy)= -siny-2xy^2=> y' = -(siny+2xy^2)/(2x^2y+xcosy)\]

Answer 2

Darn

Answer 3

y' = -(2xy^2+siny)/(2x^2y+xcosy) = -(2xy^2+siny)/x(2xy+cosy)

Answer 4

y' = (-2xy^2 - siny) / (2x^2y + xcosy)