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  • Please solve RD Sharma class 12 chapter Differentiation exercise 10.2 question 71 maths textbook solution

Please solve RD Sharma class 12 chapter Differentiation exercise 10.2 question 71 maths textbook solution

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Answer:Proved

Hint: you must know the rules of solving derivative of exponential functions.

Given:  y=e^{x}+e^{-x}

Prove: \frac{d y}{d x}=\sqrt{y^{2}-4}
 

Solution:

 y=e^{x}+e^{-x}

Differentiate with respect to x,

\frac{d y}{d x}=\frac{d}{d x}\left(e^{x}+e^{-x}\right)                    \left[\therefore \frac{d}{d x} e^{x}=e^{x} ; \frac{d}{d x} e^{-x}=-e^{-x}\right]

\begin{aligned} &\frac{d y}{d x}=e^{x}-e^{-x} \\\\ &\frac{d y}{d x}=\sqrt{\left(e^{x}-e^{-x}\right)^{2}-4 e^{x} \times e^{-x}} \end{aligned}                    \left[\therefore(a-b)=\sqrt{\left(a^{2}+b^{2}\right)-2 a b}=\sqrt{(a+b)^{2}-4 a b}\right]

\frac{d y}{d x}=\sqrt{y^{2}-4}                    [\because \left.e^{x}+e^{-x}=y\right]

∴ Proved

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