Question: 2. Let p(x) be a scalar function of a D-dimensional vector x, and f(p) be a scalar function of p. Prove that: xf[p(x)]=[dpdf(p)]xp(x) i.e., prove

2. Let p(x) be a scalar function of a D-dimensional vector x, and f(p) be a scalar function of p. Prove that: xf[p(x)]=[dpdf(p)]xp(x) 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.]

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