Show that the operation of taking the gradient of a function has the given property. Assume that u and v are differentiable functions of x and y and that a, b are constants.

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(a) V(au + bv) = a Vu + b Vv (b) V(uv) = u Vv + v Vu v Vu – u Vv %3D (d) Vu" = nu"- Vu (c) V