Differentiation Question 352
Question: If $ y=A\cos nx+B\sin nx, $ then $ \frac{d^{2}y}{dx^{2}}= $
[Karnataka CET 1996]
Options:
A) $ n^{2}y $
B) $ -y $
C) $ -n^{2}y $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ y=A\cos (nx)+B\sin (nx) $
$ \therefore dy/dx=-nA\sin (nx)+nB\cos (nx) $
Again $ \frac{d^{2}y}{dx^{2}}=-n^{2}A\cos (nx)-n^{2}B\sin (nx) $
$ =-n^{2}[A\cos (nx)+B\sin (nx)] $
Therefore $ \frac{d^{2}y}{dx^{2}}=-n^{2}y $ .
BETA
