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If y = (e^(x)+1)/(e^(x)-1), " then" (y^(...

If` y = (e^(x)+1)/(e^(x)-1), " then" (y^(2))/2 + (dy)/(dx) ` is equal to

A

1

B

`-1`

C

`-(1)/(2)`

D

`(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
`y=(e^(x)+1)/(e^(x)-1)`
`(dy)/(dx)= ((e^(x)-1)e^(x)-(e^(x)+1)e^(x))/((e^(x)-1)^(2))`
`=(e^(x)(e^(x)-1-e^(x)-1))/((e^(x)-1)^(2))= -(2e^(x))/((e^(x)-1)^(2))`
`:. (y^(2))/(2)+(dy)/(dx)=((e^(x)+1)^(2))/(2(e^(x)-1)^(2))-(2e^(x))/((e^(x)-1)^(2))`
`=((e^(x)+1)^(2)-4e^(x))/(2(e^(x)-1)^(2))= ((e^(x)-1)^(2))/(2(e^(x)-1)^(2))`
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