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

Question

3 years ago

13

sn and i.) u = sin(x1 + 2x2 + ⋯ + nxn)

1 answer:

liq [111] · Answer 1 · 2022-01-15T09:51:05+03:00

liq [111]3 years ago

6 0

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)