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

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

A

`(6x^2-2x+2)/(x^2+1)^2sin((2x-1)/(x^2+1))^2`

B

`(6x^2-2x+2)/(x^2+1)^2sin((2x-1)/(x^2+1))`

C

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

D

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

Text Solution

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The correct Answer is:
D
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TARGET PUBLICATION-DIFFERENTIATION -COMPETITIVE THINKING
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  7. If y = f(x^(2) + 2) " and " f'(3) = 5 , " then" dy/dx " at x " = 1 is

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  8. If f (x) = log(x) (log x), then f'(x) at x = e is …….. .

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  9. If f(x)=sqrt(1+cos^2(x^2)),thenf'(sqrtpi/2) is

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  10. If : f(x)=(sin^(2)x)/(1+cotx)+(cos^(2)x)/(1+tanx)," then: "f'((pi)/(4)...

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  11. d/(dx)tan^-1((1-x)/(1+x))=

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  12. If y =tan ^(-1) ((sqrt( a) -sqrt(x)) /( 1+sqrt( ax)) ) ,then (dy)/(dx)...

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  13. If y=tan^(-1)[(sinx-cosx)/(cosx-sinx)] then (dy)/(dx) is

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  14. If y= tan ^(-1) ((acos x -bsin x )/( bcos x+asin x ) ) ,then (dy)/(dx...

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  15. यदि y= sec tan ^(-1) x, तब (dy)/(dx) =

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  16. the derivative of tan^-1 (6xsqrtx)/(1-9x^3) is sqrtx g(x) then g(x) is...

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  17. If y= e^(m sin ^(-1)) x and (1-x^(2))((dy)/(dx))^(2)= Ay^(2). then ...

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  18. If y=sin^(-1)[x(1-x)-sqrtxsqrt(1-x^(2))], find (dy)/(dx),

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  19. Find (dy)/(dx) when(y-tan^(- 1))x/(1+sqrt(1-x^2))+sin[2tan^(- 1)sqrt((...

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  20. If f(x)=cot^(-1)((x^(x)-x^(-x))/(2)) then f'(1) equals

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