If y= sin px and `y_(n)` is the `n^(th)` derivative of y, then
`|{:(y,y_(1),y_(2)),(y_(3),y_(4),y_(5)),(y_(6),y_(7),y_(8)):}|` is

Options

A. 1
B. 0
C. -1
D. none of these

Explanation

To solve the problem, we need to find the value of the determinant given the function \( y = \sin(px) \) and its derivatives up to the eighth order. Let's denote the \( n^{th} \) derivative of \( y \) as \( y_n \).

### Step 1: Calculate the derivatives of \( y \)

1. **First derivative**:
\[ y_1 = \frac{dy}{dx} = p \cos(px) \]
...