Question

`"If "y= sin x +e^(x)," then "(d^(2)x)/(dy^(2))=`
A. `(-sin x +e^(x))^(-1)`
B. `(sin x - e^(x))/((cos x +e^(x))^(2))`
C. `(sin x - e^(x))/((cos x +e^(x))^(3))`
D. `(sin x + e^(x))/((cos x +e^(x))^(3))`

Answer 1

`y=sin x +e^(x)or (dy)/(dx)=cos x +e^(x)`
`"or "(dx)/(dy)=(cos x +e^(x))^(-1)" (1)"`
`therefore" "(d^(2)x)/(dy^(2))=-(cos x +e^(x))^(-2)(-sin x +e^(x))(dx)/(dy)`
Substituting the value of `(dy)/(dx)` from (1),
`(d^(2)x)/(dy^(2))=((sin x -e^(x)))/((cos x +e^(x))^(2))(cos x +e^(x))^(-1)=(sin x-e^(x))/((cos x +e^(x))^(3))`