(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

First problem: Let [tex]f(x,y) = x-y[/tex] andu= vi+wj. In which direction does the function decrease and increase the most? And whatu(all of them) satisfies D_{u}f = 0

Second problem: Let [tex]z = f(x,y)[/tex], where [tex]x = 2s+3t[/tex] and [tex]y = 3s-2t[/tex]. Determine [tex]\partial{z^2}/\partial{s^2}[/tex]

2. Relevant equations

Gradient and the chain rule

3. The attempt at a solution

For the first question in the first problem I've gotten using gradient: increasei-jand decrease -i+j. Am I correct? For the second question all I've gotten so far is (nabla)f(dot)u= 0 = (1-y)v+(x-1)w. Where do I get the second equation to solve both v and w?

Second problem gives me 4z_{xx}+12z_{xy}+9z_{yy}. Is that completely wrong?

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# Homework Help: Partial derivatives.

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