Problem 3 (3.5+2.5–6 Marks). Let uv,w:R3 R be three smooth functions and for any function : R3 R let us use fri fy and f

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Problem 3 3 5 2 5 6 Marks Let Uv W R3 R Be Three Smooth Functions And For Any Function R3 R Let Us Use Fri Fy And F 1 (16.15 KiB) Viewed 12 times

Problem 3 (3.5+2.5–6 Marks). Let uv,w:R3 R be three smooth functions and for any function : R3 R let us use fri fy and f: to respectively denote the partial derivative off with respect to r, y and . Then provide all the details and show the following two identities: d(uda + vdy + wdz) = (wy - v.) dy Adz + (u: - w.)dz do +(Us - u) do A dy, d(udy, dz + vda A dx + wdx Ady) = (x + y +w.)dx dy dz.