If `y=e^x+e^-x`, prove that `(dy)/(dx)=sqrt(y^2-4)`

Explanation

We have, `y=e^x+e^-x`

Differentiate it with respect to `mathrmx`,

`(d y)/(d x) =d/(d x)(e^x+e^-x)`

`=d/(d x) e^x+d/(d x) e^-x`

`=e^x+e^-x d/(d x)(-x) quad text [Using chain rule]`

`=e^x+e^-x(-1)`

`=(e^x-e^-x)`

`=sqrt((e^x+e^-x)^2-4 e^x times e^-x )quad[therefore(a-b)=sqrt((a+b)^2-4 a b)]`

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