(a) Let p(x) be a scalar function of a D-dimensional vector x, and f(p) be a scalar function of p. Prove that: v.S[P(x)]

[answerhappygod]

A Let P X Be A Scalar Function Of A D Dimensional Vector X And F P Be A Scalar Function Of P Prove That V S P X 1 (36.33 KiB) Viewed 58 times

(a) Let p(x) be a scalar function of a D-dimensional vector x, and f(p) be a scalar function of p. Prove that: v.S[P(x)]=[, "(m). Pla) i.e., prove that the chain rule applies in this way. (Hint: you can show it for the ith component of the gradient vector, for any i. It can be done in a couple lines.] (b) Use relation (4) of “expressions” in Discussion 2, to find V_(xPx). (C) Prove your result of V_(x?a) in part (b) by, instead, writing out the components. (d) Use (a) and (b) to find 2)] in terms of x V (a) Use relations above to find ... Express your answer in terms of Hell where possible. Hint: let p=w'w; what is f? (b) Find: .||Mw– bly Express your result in simplest form. Hint: first choose p (remember it must be a scalar).