1.

If `y=x+e^x ,`then `(d^2x)/(dy^2)`is equal toA. `e^(x)`B. `-(e^(x))/((1+e^(x))^(3))`C. `-(e^(x))/((1+e^(x))`D. `(e^(x))/((1+e^(x))^(2))`

Answer» Correct Answer - B
Givne that `y=x+e^(x)`
Differentiating w.r.t. x
`(dy)/(dx)=1+e^(x)`
`rArr" "(dx)/(dy)=(1)/(1+e^(x))`
Differentiating w.r.t. y
`(d^(2)x)/(dy^(2))=-((1)(e^(x)))/((1+e^(x))^(2)).(dx)/(dy)`
`=-(e^(x))/((1+e^(x))^(2)).(1)/((1+e^(x)))=-(e^(x))/((1+e^(x))^(3))`


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