Question

If $y=\sin px$ and $y_n$ is the $n$th derivative of $y$, then $\left|\begin{array}{ccc}y& y_1& y_2\\ y_3& y_4& y_5\\ y_6& y_7& y_8\end{array}\right|$ is equal to

• A. $1$
• B. $0$
• C. $-1$
• D. None of these

Answer 1

The correct option is B $0$

$D=\left|\begin{array}{ccc}\sin px& p\cos px& -p^2\sin px\\ -p^3\cos px& p^4\sin px& p^5\cos px\\ -p^6\sin px& -p^7\cos px& p^8\sin px\end{array}\right|$
$=p^9\left|\begin{array}{ccc}\sin px& p\cos px& -p^2\sin px\\ -\cos px& p\sin px& p^2\cos px\\ -\sin px& -p\cos px& p^2\sin px\end{array}\right|$
$=-p^9\left|\begin{array}{ccc}\sin px& p\cos px& -p^2\sin px\\ \cos px& p\sin px& p^2\cos px\\ \sin px& p\cos px& -p^2\sin px\end{array}\right|=0$