Jacobian matrix of partial derivatives

Let ‘u’ and ‘v’ be functions of two independant variables ‘x’ and ‘y’.

The jacobian(J) of ‘u’ and ‘v’ with respect to ‘x’ and ‘y’ is symbolically represented and defined as follows

Jacobian matrix problems

  1. If u=yz/x, r=zx/y, w=xy/z, Show that J [(u, v, w)/ (x, y, z)] =4
  2. If u=x+3y^2, v=4x^2 yz, w=2z^2-xy, Evaluate del (u,v,w)/del (x,y,z) at the point (1,-1, 0)
  3. If u=(x_2 x_3)/x_1, v=(x_1 x_3)/x_2, w=(x_1 x_2)/x_3 find the value of Jacobian J del (u,v,w)/del(x_1,x_2,x_3)
  4. If u=x^2+y^2+z^2, v=xy+yz+zx, w=x+y+z find the value of Jacobian J del(u,v,w)/ del(x,y,z)
  5. If u=x+y+z, uv=y+z,uvw=z, then find ∂(x,y,z)/∂(u,v,w)




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