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y=f((2x-1)/(x^2+1))andf^'(x)=sinx^2 the...

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

Text Solution

Verified by Experts

The correct Answer is:
`(-2(x^(2)-x-1))/((x^(2)+1)^(2))* sin^(2) ((2x-1)/(x^(2)+1))`
Given, ` y= f((2x-1)/(x^(2)+1))`
and ` f'(x) = sin^(2) x`
` :." "(dy)/(dx) = f'((2x-1)/(x^(2)+1)) *d/(dx) ((2x-1)/(x^(2)+1)) `
`=sin^(2)((2x-1)/(x^(2)+1))*{((x^(2)+1)*2-(2x-1)(2x))/((x^(2)+1)^(2))}`
`= sin^(2)((2x-1)/(x^(2)+1))*(-2x^(2)+2x+2)/((x^(2)+1)^(2))`
` = (-2(x^(2)-x-1))/((x^(2)+1)^(2))sin^(2)((2x-1)/(x^(2)+1))`
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