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

`"If "y=(x^(2))/(2)+(1)/(2)xsqrt(x^(2)+1)+log_(e)sqrt(x+sqrt(x^(2)+1)),` then

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

AI Generated Solution

To find the derivative of the function given by \[ y = \frac{x^2}{2} + \frac{1}{2} x \sqrt{x^2 + 1} + \log_e \sqrt{x + \sqrt{x^2 + 1}}, \] we will differentiate each term step by step. ...
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