Let z=e^−y cos x. Show that (∂^2z)/(∂x^2)+(∂^2z)/(∂y^2) = 0?
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∂z/∂x = -e^(-y) sin x
∂²z/∂x² = -e^(-x) cos x.
∂z/∂y = -e^(-y) cos x
∂²z/∂y² = e^(-y) cos x.
Therefore,
∂²z/∂x² + ∂²z/∂y² = -e^(-x) cos x + e^(-y) cos x = 0.
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