Problem 3 (3.5+2.5=6 Marks). Let u, v, w : R3 R be three smooth functions and for any function f : R3 → R let us use fx,

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Problem 3 3 5 2 5 6 Marks Let U V W R3 R Be Three Smooth Functions And For Any Function F R3 R Let Us Use Fx 1 (41.53 KiB) Viewed 14 times

Problem 3 (3.5+2.5=6 Marks). Let u, v, w : R3 R be three smooth functions and for any function f : R3 → R let us use fx, fy and fz to respectively denote the partial derivative of f with respect to x, y and z. Then provide all the details and show the following two identities: d(udx + vdy + wdz) = (w, – vz) dy 1 dz + (uz – wą) dz 1 dx + (vx – uy) dx A dy, d(udy 1 dz + vdz 1 dx + wdx / dy) = (uz + Vy + wz)dx A dy A dz.