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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

Answers (1)

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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