Home
Class 12
MATHS
d/(dx)sqrt((1-sin2x)/(1+sin2x))i se q u ...

`d/(dx)sqrt((1-sin2x)/(1+sin2x))i se q u a lto,(0

A

`sec^(2)x`

B

`-sec^(2)((pi)/(4)-x)`

C

`sec^(2)((pi)/(4)+x)`

D

`sec^(2)((pi)/(4)-x)`

Text Solution

Verified by Experts

`y=sqrt((1-sin 2x)/(1+ sin 2x))=(cos x - sin x)/(cos x + sin x)=(1-tan x)/(1+ tan x)=tan ((pi)/(4)-x)`
`therefore (dy)/(dx)=-sec^(2)((pi)/(4)-x)`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise (Multiple)|22 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise (Comprehension)|23 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise 3.9|14 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|25 Videos

  • DOT PRODUCT

    CENGAGE|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

(d)/(dx)(sqrt(x sin x))=?

sqrt((1+sin x)/(1-sin x)) Differentiate w.r.t x

Differentiate log sqrt((1+sin x)/(1-sin x)) with respect to x:

Differentiate sqrt((1+sin x)/(1-sin x)) with respect to x:

(d)/(dx)[sin^(-1)sqrt(((1-x))/(2)]=

(d)/(dx)(ln sin sqrt(x)) equals to-

(d)/(dx)(sqrt(x)+(1)/(sqrt(x)))^(2) =

d//dx[sin^(2)cot^(-1)""(1)/(sqrt((1+x)/(1-x)))] , is equal to -

CENGAGE-DIFFERENTIATION-Exercise (Single)
  1. A function f: RvecR satisfies xcosy(f(2x+2y)-f(2x-2y)=cosxsiny(f(2x+2y...

    Text Solution

    |

  2. If y=asinx+bcosx , then y^2+((dy)/(dx))^2 is a

    Text Solution

    |

  3. d/(dx)sqrt((1-sin2x)/(1+sin2x))i se q u a lto,(0<x<pi/2), sec^2x (b) ...

    Text Solution

    |

  4. If f(x) = |cos x| + |sin x|, then dy/dx at x = (2pi)/3 is equal to

    Text Solution

    |

  5. If f(x) =|log(e)|x||, then f'(x) equals

    Text Solution

    |

  6. If f(x)=sqrt(1-sin2x) , then f^(prime)(x) is equal to -(cosx+sinx),for...

    Text Solution

    |

  7. Instead of the usual defination of derivatie Df(x), if we define a new...

    Text Solution

    |

  8. if y=((a-x)sqrt(a-x)-(b-x)sqrt(x-b))/(sqrt(a-x)+sqrt(x-b)) then dy/dx ...

    Text Solution

    |

  9. The derivative of y=(1-x)(2-x)..........(n-x) at x=1 is equal to

    Text Solution

    |

  10. " If "y=sqrt((1-x)/(1+x))," then "(1-x^(2))(dy)/(dx) is equal to

    Text Solution

    |

  11. If y=(sqrt(a+x)-sqrt(a-x))/(sqrt(a+x)+sqrt(a-x)), then (dy)/(dx) is e...

    Text Solution

    |

  12. Let u/x a n dv(x) be differentiable functions such that (u(x))/(v(x))=...

    Text Solution

    |

  13. If sin^(-1)((x^2-y^2)/(x^2+y^2))=loga ,t h e n(dy)/(dx) is equal to x/...

    Text Solution

    |

  14. Let h(x) be differentiable for all x and let f(x)=(k x+e^x)h(x) , wher...

    Text Solution

    |

  15. If lim(trarrx) (e^(t)f(x)-e^(x)f(t))/((t-x)(f(x))^(2))=2 andf(0)=(1)/(...

    Text Solution

    |

  16. If f(0)=0,f^(prime)(0)=2, then the derivative of y=f(f(f(x))) at x=0 i...

    Text Solution

    |

  17. If f(x)=sqrt(1+cos^2(x^2)),t h e nf^(prime)((sqrt(pi))/2) is (sqrt(pi)...

    Text Solution

    |

  18. (d)/(dx)cos^(-1)sqrt(cosx),0ltxlt(pi)/(2) is equal to

    Text Solution

    |

  19. If t a n y=(2^x)/(1+2^(2x+1)),t h e n(dy)/(dx)a tx=0i s -3/(10) ...

    Text Solution

    |

  20. If y=(x+sqrt(x^2+a^2))^n ,t h e n(dy)/(dx) is (n y)/(sqrt(x^2+a^2)) (b...

    Text Solution

    |