If \( y=500e^{7x}+600e^{-7x} \), then \( \displaystyle\frac{d^2y}{dx^2} \) equals :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 49(500e^{7x}+600e^{-7x}) \)
Each differentiation of \( e^{7x} \) brings out a factor 7, and each differentiation of \( e^{-7x} \) brings out a factor −7.
\( \displaystyle \frac{dy}{dx}=3500e^{7x}-4200e^{-7x} \)
\( \displaystyle \frac{d^2y}{dx^2}=24500e^{7x}+29400e^{-7x} \)
\( \displaystyle =49(500e^{7x}+600e^{-7x}) \)
Tip: For \( y=Ae^{kx}+Be^{-kx} \), \( \frac{d^2y}{dx^2}=k^2y \). Here \( k=7 \), so the answer is simply 49y.
NCERT (2026-27 edition):
Second Order Derivative
