If `y=f((2x-1)/(x^2+1))`and`f^'(x)=sinx^2`, then find `(dy)/(dx)`

Options

A. `sin((2x-1)/(x^(2)+1))^(2){(x^(2)+2x+2)/((x^(2)+1))}`
B. `sin((2x-1)/(x^(2)+1))^(2){(2+2x-2x^(2))/((x^(2)+1)^(2))}`
C. `sin((2x-1)/(x^(2)+1))^(2){(2+2x-x^(2))/((x^(2)+1)^(2))}`
D. none of these

Answer

B

Explanation

We have,
`y=f((2x-1)/(x^(2)+1))`
`implies" "(dy)/(dx)=f'((2x-1)/(x^(2)+1))(d)/(dx)((2x-1)/(x^(2)+1))`
`implies" "(dy)/(dx)=f'((2x-1)/(x^(2)+1))^(2){(2(x^(2)+1)-2x(2x-1))/((x^(2)+1)^(2))}`
`" "[becausef'(x)=sinx^(2)]`
`implies" "(dy)/(dx)=sin((2x-1)/(x^(2)+1))^(2){(2+2x-2x^(2))/((x^(2)+1)^(2))}`