Find `(dy)/(dx) for y=log(x+sqrt(a^2+x^2))dot`

Explanation

`y=log (x+sqrt(a^(2)+x^(2)))`
`"Then "(dy)/(dx)=(d)/(x){log (x+sqrt(a^(2)+x^(2)))}`
`=(1)/(x+sqrt(a^(2)+x^(2)))(d)/(dx)(x+sqrt(a^(2)+x^(2)))`
`=(1)/(x+sqrt(a^(2)+x^(2)))xx{1+(1)/(2)(a^(2)+x^(2))^(-1//2)(d)/(dx)(a^(2)+x^(2))}`
`=(1)/(x+sqrt(a^(2)+x^(2))){1+(1)/(2sqrt(a^(2)+x^(2)))xx2x}`
`(1)/(x+sqrt(a^(2)+x^(2)))xx(sqrt(a^(2)+x^(2))+x)/(sqrt(a^(2)+x^(2)))`
`=(1)/(sqrt(a^(2)+x^(2)))`