Home
Class 12
MATHS
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

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

B

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

C

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

D

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

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

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

If y=f((2x-1)/(x^(2)+1)) and f^(')(x)=sinx^(2) then dy//dx at x=0 is

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

If y = f((2x-1)/(x^(2)+1))and f'(x) = sin^(2) x, " then " (dy)/(dx) = ……. .

If f'(x)=sqrt(2x^(2)-1) and y=f(x^(2)), then (dy)/(dx) at x=1 is equal to 2b 1c.-2d.-1

If f'(x)=sqrt(2x^(2)-1) and f(x^(2)), then (dy)/(dx) at x=1 is equal to 2(b)1(c)-2(d)-1

If f^(1)(x)=(1)/(1+(ln x)^(2)) and y=f(e^(tan x)) then (dy)/(dx) is equal to

If f(x)=sqrt(3x^(2)+6) and y=f(x^(3)), then at x=1,(dy)/(dx) is equal to

If y=f(x^(3)),z=g(x^(2)),f'(x),=cosx and g'(x)=sinx," then "(dy)/(dz) is

ALLEN-TEST PAPERS-MATHEMATICS
  1. If Lim(x to 0)(ae^(x)-bln(1+x)+ce^(-x))/(x sin x)=2 then value of a+b+...

    Text Solution

    |

  2. "If "f(x)=(x-1)^(4)(x-2)^(3)(x-3)^(2)(x-4), then the value of f'''(1)+...

    Text Solution

    |

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

    Text Solution

    |

  4. f:RtoR such that f(2)=5 and f'(2)=10 thenlim(xto0) ((f(2+x))/(f(2)))^(...

    Text Solution

    |

  5. The value of lim(xto0^(+))(x^(x)+(tanx)^(cosecx)+(cosecx)^(tanx)) is...

    Text Solution

    |

  6. f:RtoR is defined as f(x)=x^(3)+2x^(2)+7x+cos(pix) and g be the invers...

    Text Solution

    |

  7. Let f(x) be a cubic polynomical such that f'(x)=0 at x=1 and x=3, f(1)...

    Text Solution

    |

  8. lim(xto oo)(ln(x^(2)+5x)-2ln(cx+1)=-2 then

    Text Solution

    |

  9. The variable x satisfying the equation |sinxcosx|+sqrt(2+tan^2+cot^2x)...

    Text Solution

    |

  10. If quadratic equation (1+m)x^(2)-2(1+3m)x-2(1+m)=0 has one root greate...

    Text Solution

    |

  11. The quadratic polynomial p(x) has the following properties:p(x)geq0 fo...

    Text Solution

    |

  12. Domain off(x)=log(x^2+5x+6)/([x]-1)where [.] denotes greatest integer ...

    Text Solution

    |

  13. Let f:RtoR f(x)=x+3x^(3)+5x^(5)+………..+1001x^(1001) then which of fol...

    Text Solution

    |

  14. The vaue of x satisfying sin^(-1)(x)+sin^(-1)(sqrt(15)x)=(pi)/2 is

    Text Solution

    |

  15. The sum sum(n=1)^oo tan^(-1)(3/(n^2+n-1)) is equal to

    Text Solution

    |

  16. Range of f(x)=sin^(-1)x+tan^(-1)x+sqrt(x+1) is [a,b] then b+a is equal...

    Text Solution

    |

  17. Let f(x)={(cos[x],xge0),(|x|+a,xlt0):} (where [.] denotes greatest i...

    Text Solution

    |

  18. lim(nto oo) (1-1/(2^(2)))(1-1/(3^(2)))(1-1/(4^(2)))…………….(1-1/(n^(2)))...

    Text Solution

    |

  19. The velue of lim(x->0)(sin(3sqrtx)ln(1+3x))/((tan^(- 1)sqrt(x))^2(e^(...

    Text Solution

    |

  20. Let f:RtoR is given by f(x)={(p+qx+x^(2),xlt2),(2px+3qx^(2),xge2):} t...

    Text Solution

    |