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Find the first partial derivatives of the function. (sn = x1 + 2x2 + ... + nxn; i = 1, ..., n. give your answer only in terms of sn and i.) u = sin(x1 + 2x2 + ⋯ + nxn)

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sqdancefan

Answer:

  ∂u/∂xi = i·cos(sn)

Step-by-step explanation:

For u = sin(v), the partial derivative of u with respect to xi is ...

  ∂u/∂xi = cos(v)·∂v/xi

In this case, v=sn, and ∂sn/∂xi = i, so the derivatives of interest are ...

  ∂u/∂xi = i·cos(sn)

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