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left parenthesis, x, y, squared, plus, x, right parenthesis, d, x, plus, left parenthesis, y, x, squared, plus, y, right parenthesis, d, y, equals, 0
Solve for d
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Solve for x
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\left(xy^{2}d+xd\right)x+\left(yx^{2}+y\right)dy=0
Use the distributive property to multiply xy^{2}+x by d.
y^{2}dx^{2}+dx^{2}+\left(yx^{2}+y\right)dy=0
Use the distributive property to multiply xy^{2}d+xd by x.
y^{2}dx^{2}+dx^{2}+\left(yx^{2}d+yd\right)y=0
Use the distributive property to multiply yx^{2}+y by d.
y^{2}dx^{2}+dx^{2}+x^{2}dy^{2}+dy^{2}=0
Use the distributive property to multiply yx^{2}d+yd by y.
2y^{2}dx^{2}+dx^{2}+dy^{2}=0
Combine y^{2}dx^{2} and x^{2}dy^{2} to get 2y^{2}dx^{2}.
\left(2y^{2}x^{2}+x^{2}+y^{2}\right)d=0
Combine all terms containing d.
\left(2x^{2}y^{2}+x^{2}+y^{2}\right)d=0
The equation is in standard form.
d=0
Divide 0 by 2y^{2}x^{2}+x^{2}+y^{2}.