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

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

A

`sin((2x-1)/(x^(2)+1)^(2).((2+2x+2x^(2))/((x^(2)+1)^(2))))`

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

`sin(x^(2)).((2+2x-2x^(2))/((x^(2)+1)^(2)))`

Text Solution

Verified by Experts

The correct Answer is:
B
`y=f((2x-1)/(x^(2)+1)),(dy)/(dx)`
`=f^(')((2x-1)/(x^(2)+1)).((x^(2)+1)/2-(2x-1).2x)/((x^(2)+1)^(2))`
`=sin((2x-1)/(x^(2)+1))^(2).(-2x^(2)+2x+2)/((x^(2)+1)^(2))`
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