Question
7. (1pt) Let u = f(x, y), x = X(s,t), y = Y(s, t), then u is a function of s, t, call it = F ( s, t ) . u = (a) Write ᎧF /Ꭷs and ᎧF Ꭷt in terms of ò f / ox, Ꭷf /òy, ᎧX/Zs, ᎧX /0t, ᎧY /Ꭷs, and ᎧY Ꭷt. (b) Suppose that 0- f / (Zxy) = 8-f / (òyò), show that = ᎧF ò f 82 X ds2 Ꭷr ds2 0x2 = + 4 ( ) - f ( 8X მs f მs მs მrმყი მ
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