If $$u^3=xyz, \frac 1v=\frac1x+\frac1y+\frac 1z, w^2= x^2+y^2+z^2$$, then prove that
$$\frac{\partial(u,v,w)}{\partial(x,y,z)}=\frac{v(y-z)(z-x)(x-y)(x+y+z)}{3u^2w(yz+zx+xy)}$$
2026-02-22 19:27:20.1771788440
Finding Jacobian of implicit function.
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Sorry friends! Finally, I caught the point where I was missing. It was $$v^2$$ which was to be partially replaced with $$\frac{xyz}{xy+yz+zx}$$ in the expression which was preventing to reach at the desired result. Thanks for your humble suggestions.