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

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

Answers (1)

Answer:

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}

Posted by

Gurleen Kaur

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