यदि `y=(xsin^(-1)x)/(sqrt(1-x^(2)))+log_(e)sqrt(1-x^(2))` है तो `((d^(2)y)/(dx^(2)))_(x=0)` बराबर है

Options

A. `0`
B. `1`
C. `(1)/(2)`
D. `2`

Answer

B

Explanation

दिया है,

`y=(xsin^(-1)x)/(sqrt(1-x^(2)))+(1)/(2)log(1-x^(2))`

`:." "(dy)/(dx)=1*(sin^(-1)x)/(sqrt(1-x^(2))+x)`

`{(1)/(sqrt(1-x^(2)))*(1)/(sqrt(1-x^(2)))+(-1)/(2)*(1)/((1-x^(2))^(3//2))(-2x)sin^(-1)x}+(1)/(2)*((-2x))/((1-x^(2)))`

`(dy)/(dx)=(sin^(-1)x)/(sqrt(1-x^(2)))+x^(2)*(sin^(-1)x)/((1-x^(2))^(3//2))`

`:." "(d^(2)y)/(dx^(2))=(1)/(1-x^(2))+sin^(-1)x(d)/(dx)((1)/(sqrt(1-x^(2))))+2x*(sin^(-1)x)/((1-x^(2))^(3//2))``+x^(2)(d)/(dx){:[((sin^(-1)x))/((1-x^(2))^(3//2))]:}``+x^(2){(1)/((1-x^(2))^(2))``+(3sin^(-1)x)/((1-x^(2))^(5//2))*x}`

`:." "((d^(2)y)/(dx^(2)))_(x=0)=1+0+0+0=1`