1 Read carefully the definition of interpolation polynomial, the function value of f(x) and several tables of derivative values.

Understand the meaning of ni and mj.

2 when Ni = 1L, J = 0. Note that t-xi = xi-xi = 0.

Obviously, ω = 0.

3 When Ni = 2, j≤ 1, take the derivative, and note that t-xi = xi-xi = 0, we can see that ω and its derivative are still equal to 0.

When ni≥3 and j≤ni- 1, as mentioned above, it can be seen that ω and its derivative are still equal to 0.

............................................

1 Read carefully the definition of interpolation polynomial, the function value of f(x) and several tables of derivative values.

Understand the meaning of ni and mj.

According to the definition of interpolation polynomial:

F(xi) and its derivative -pn(xi) and its derivative =0

Namely: φ(xi) and the first part of its derivative =0.

2 φ(xi) and the second part of its derivative =0

When Ni = L and J = 0, it is 2. 1. Note that t-xi = xi-xi = 0. Obviously, ω (xi) = 0.

2.2 when Ni = 2, j≤ 1, find the derivative, and note that t-xi = xi-xi = 0, we can see that ω(xi) and its derivative are still equal to 0.

2.3 when ni≥3, j≤ni- 1. As mentioned above, it can be seen that ω(xi) and its derivative are still equal to 0.

3 To sum up, φ(xi) and its derivative =0.