cosx^2/y^2 - xy = y/x^2
y=(cosx^2/y^2 -xy) x^2
dy/dx =(cosx^2/y^2 -xy) x^2
Applying product rule as: (f\cdot g)^'=f^'\cdot g+f\cdot g^'
f=\frac{\cos (x^2)}{y^2}-xy, g=x^2
=\frac{d}{dx}(\frac{\cos (x^2)}{y^2}-xy)x^2+\frac{d}{dx}(x^2)(\frac{\cos \(x^2)}{y^2}-xy)
\frac{d}{dx}(\frac{\cos (x^2\)}{y^2}-xy) = =-\frac{2x\sin(x^2)}{y^2}-y
(Applying sum/difference rule as: (f\pm g)^'=f^'\pm g^'
=\frac{d}{dx}(\frac{\cos(x^2)}{y^2})-\frac{d}{dx}(xy)
Here,
=\frac{d}{dx}(\frac{\cos(x^2)}{y^2}) = -\frac{2x\sin(x^2)}{y^2}
and,
\frac{d}{dx}(xy) = y)
=-\frac{2x\sin (x^2)}{y^2}-y
Again,
\frac{d}{dx}(x^2)=2x
Finally,
=(-\frac{2x\sin(x^2)}{y^2}-y)x^2+2x(\frac{\cos (x^2)}{y^2}-xy)
Simplifying it,
=\frac{x(-3xy^3-2x^2\sin (x^2)+2\cos (x^2))}{y^2}
