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Kruum
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Homework Statement
First problem: Let [tex]f(x,y) = x-y[/tex] and u = vi+wj. In which direction does the function decrease and increase the most? And what u (all of them) satisfies Duf = 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]
Homework Equations
Gradient and the chain rule
The Attempt at a Solution
For the first question in the first problem I've gotten using gradient: increase i-j and 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 4zxx+12zxy+9zyy. Is that completely wrong?
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