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If y=(x^2)/2+1/2xsqrt(x^2+1)+1/2(log)esq...

If `y=(x^2)/2+1/2xsqrt(x^2+1)+1/2(log)_esqrt(x+sqrt(x^2+1))` , prove that `2y=x y^(prime)+(log)_e y^(prime),w h e r ey '` denotes the derivative w.r.t `xdot`

A

`y'=x+sqrt(x^(2)+1)`

B

`y'=(1)/(x+sqrt(x^(2)+1))`

C

`2y=xy'+log_(e)y'`

D

`2y=xy'-log_(e)y'`

Text Solution

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To prove that \[ 2y = xy' + \log_e y' \] where ...
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