Question

U=2(x2+Y2) V=3(X2+Y2) THE FIND D (U,V)D(X,Y)

Answer 1

Answer:

du = 2x dx - 2y dy, and dv = y dx + x dy. When v is constant, i.e. dv = 0, one has dy = -(y/x) dx, and hence du = (2x + 2y2/x) dx. I.e.,

(∂x/∂u)v = x/[2(x2 + y2)]