Question

if u= x+y and v= x/x+y then y equal to​

Answer 1

Answer:

Suppose that x and y are two independent variables which can be expressed in terms of two other independent variables u and v by the formula x = g(u,v) and y = h(u,v). The Jacobian of x and y with respect to u and v, J(u,v), is

J(u,v) =

| (dx/du) (dx/dv) |

Det | (dy/du) (dy/dv) |

= (dx/du)(dy/dv) - (dy/du)(dx/dv)"

where d represents a partial derivative.

From this, all we need to do to continue is swap: x,y <-> u,v. This reduces the need for quotient rule and/or nasty expressions using non-elementary functions to express x or y strictly in terms of u and v.

Thus, x = uv and y = uv^3.

dx/du = v

dx/dv = u

dy/du = v^3

dy/dv = 3uv^2

So J(u,v) = (v)(3uv^2) - (u)(v^3) = 3uv^3 - uv^3 = 2uv^3.