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If y=e^x+e^(-x),"p r o v et h a t"(dy)/...

If `y=e^x+e^(-x),"p r o v et h a t"(dy)/(dx)=sqrt(y^2-4)`

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Let `y=e^x+e^(−x)`
`dy/dx=e^x-e^(−x)`
`y^2=e^(2x)+e^(−2x)+2`
`y^2-4=e^(2x)+e^(−2x)-2`
=`sqrt(y^2-4)=|e^x-e^(-x)|`
or,`(dy)/(dx)=sqrt(y^2-4)`
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RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
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