If y = A sin x + B cos x, where A and B are constants, then \(\displaystyle\frac{d^2y}{dx^2}\) is equal to:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → −y
Differentiating y = A sin x + B cos x once:
\( \displaystyle \frac{dy}{dx} = A\cos x - B\sin x \)
Differentiating again gives the second derivative:
\( \displaystyle \frac{d^2y}{dx^2} = -A\sin x - B\cos x \)
\( = -(A\sin x + B\cos x) \)
\( = -y \)
NCERT (2026-27 edition):
Second Order Derivative
