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If $f(x,y) = \cos(cx+y) + e^{cx-y}$ Show $f_{xx}=c^{2}f_{yy}$ My try, $$f_{x}=-c\sin(cx+y)+ce^{cx-y}$$ $$f_{xx}=-c^{2}\cos(cx+y)+c^{2}e^{cx-y}$$ $$f_{y}=-\sin(cx+y)-e^{cx-y}$$ $$f_{yy}=-\cos(cx+y)+e^{cx-y}$$ So,$$ f_{xx}=c^2(-\cos(cx+y)+e^{cx-y})$$ so, $$f_{xx}=c^2f_{yy}$$ Is this approach correct? Is there another approach to show this?

mathlove
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Socre
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    Your approach is correct and good enough. I don't think you'll be able to find another approach as direct, efficient, or easy as the one you've already taken. – layman May 15 '15 at 21:30

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