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#### Need solution for RD Sharma maths class 12 chapter Higher Order Derivatives exercise 11.1 question 35

Proved

HInt:

You must know the derivative of exponential function

Given:

$y=500 e^{7 x}+600 e^{-7 x}, \text { show } \frac{d^{2} y}{d x^{2}}=49 y$

Solution:

$y=500 e^{7 x}+600 e^{-7 x}$

\begin{aligned} &\frac{d y}{d x}=(7)(500) e^{7 x}+(-7)(600) e^{-7 x} \\ &\frac{d^{2} y}{d x^{2}}=(7)(7)(500) e^{7 x}+(-7)(-7)(600) e^{-7 x} \\ &\frac{d^{2} y}{d x^{2}}=(49)(500) e^{7 x}+(49)(600) e^{-7 x} \\ &\frac{d^{2} y}{d x^{2}}=(49)\left[(500) e^{7 x}+(600) e^{-7 x}\right] \\ &\frac{d^{2} y}{d x^{2}}=49 y \end{aligned}
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