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**linalg123** Suppose that the functions u and v are harmonic in a domain D:

(a) Is the product uv necessarily harmonic in D?

(b) Is du/dx harmonic in D? (You may use the fact that harmonic functions have continuous

partial derivatives of all orders.)

In the previous question i have shown that if v is harmonic conjugate for u in a domain D, then uv is harmonic in D.

Now i'm assuming that uv is only harmonic in D if v is harmonic conjugate for u, but can u and v both be harmonic without being conjugate of the other? If so, can someone tell me how to explain it in words in a general sense without actually being given specific values for u or v.

For b) i think it will be harmonic if u_{xxx} + u_{xyy }= 0.