Question

If $y=\sin mx$ , then the value of the $y_1{y}_2{y}_3$ is=? Where $y_n=\frac{d^{n}y}{d{x}^n}$ is

• A. $m^2$
• B. $m^3$
• C. $m^9$
• D. None of these

Answer 1

Answer: (D)

None of these

Here, $y=\sin mx$

$y_1=\frac{dy}{dx}=m\cos mx$

$y_2=\frac{d^{2}y}{d{x}^2}=-m^2\sin mx$

$y_3=\frac{d^{3}y}{d{x}^3}=-m^3\cos mx$

Hence,

$y_1{y}_2{y}_3=\left(m\cos mx\right)(-m^2\sin mx)(-m^3\cos mx)=m^6{\cos }^{2}mx\sin mx$