Partial Differentiation Example of total Differentiation If z=f(x, y) and x=e^u cos(v), y=e^u sin(v)

@Swati Theng Mathematics
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example if z = f(x, y) and x=e^u cos(v), y=e^u sin(v) then prove that (𝜕𝑧/𝜕𝑢)^2+(𝜕𝑧/𝜕𝑣)^2=𝑒^2𝑢 [(𝜕𝑧/𝜕𝑥)^2+(𝜕𝑧/𝜕𝑦)^2 ]
solution If 𝑧=𝑓(𝑥, 𝑦) and 𝑥=𝑒^𝑢 cos⁡𝑣, 𝑦=𝑒^𝑢 sin⁡𝑣 then prove that (𝜕𝑧/𝜕𝑢)^2+(𝜕𝑧/𝜕𝑣)^2=𝑒^2𝑢 [(𝜕𝑧/𝜕𝑥)^2+(𝜕𝑧/𝜕𝑦)^2 ]
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[theguy_z]

thank you!, i like how theyre making us do such paragraphs of answers as homewrok .hahahha