Home
Class 12
MATHS
If y=sin[2tan^(-1){sqrt((1-x)/(1+x))}],...

If `y=sin[2tan^(-1){sqrt((1-x)/(1+x))}],`find`(dy)/(dx)`

Text Solution

AI Generated Solution

To find the derivative \(\frac{dy}{dx}\) for the function \[ y = \sin\left[2 \tan^{-1}\left(\sqrt{\frac{1-x}{1+x}}\right)\right], \] we will follow these steps: ...
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIALS, ERRORS AND APPROXIMATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|102 Videos
  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA|Exercise Solved Examples And Exercises|67 Videos

Similar Questions

Explore conceptually related problems

y=tan^(-1)sqrt((1-x)/(1+x))find(dy)/(dx)

If y=tan^(-1)((1-x)/(1+x)), find (dy)/(dx)

(iv) If y=tan^(-1)(x/(1+sqrt(1-x^(2))))+sin(2tan^(-1)sqrt((1-x)/(1+x))) , then find (dy)/(dx) for x epsilon(-1,1)

If y=sin^(-1){(sqrt(1+x)-sqrt(1-x))/(2)} , find (dy)/(dx).

If y=(x sin^(-1)x)/(sqrt(1-x^(2))), find (dy)/(dx).

If y=tan^(-1)((sqrt(1+x^(2))-1)/(x)) , then find (dy)/(dx) when -1lexle1.

If y = tan ^(-1) (sqrt((1+cos x)/(1-cos x))), " find " (dy)/(dx)

If y=sin^(-1)x+sin^(-1)sqrt(1-x^(2)) then find (dy)/(dx)

y=tan^(-1)sqrt(x)then-(dy)/(dx)=

If y =sin ^(-1) sqrt((1+x^(2))/( 2) ),then (dy)/(dx) =

RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. Differentiate the functions with respect to x : cos^(-1){(cosx+sinx...

    Text Solution

    |

  2. If the derivative of tan^(-1)(a+b x) takes the value 1 at x=0, prove t...

    Text Solution

    |

  3. If y=sin[2tan^(-1){sqrt((1-x)/(1+x))}],find(dy)/(dx)

    Text Solution

    |

  4. If log(x^2+y^2)=2tan^(-1)(y/x), show that (dy)/(dx)=(x+y)/(x-y) .

    Text Solution

    |

  5. If y=cos^(-1)(2x)+2cos^(-1)sqrt(1-4x^2),-1/2<x<0 , find (dy)/(dx)

    Text Solution

    |

  6. If sqrt(1-x^6)+sqrt(1-y^6)=a(x^3-y^3),p rov et h a t(dy)/(dx)=(x^2)/(...

    Text Solution

    |

  7. If cos^(-1)((x^2-y^2)/(x^2+y^2))=tan^(-1)a , prove that (dy)/(dx)=y/xd...

    Text Solution

    |

  8. Differentiate cos^(-1)(1-2x^2) with respect to x , if 0<x<1 (ii) -1<x...

    Text Solution

    |

  9. Differentiate tan^(-1)((3x-x^3)/(1-3x^2)),if -1/sqrt(3)ltxlt1 /sqrt...

    Text Solution

    |

  10. Differentiate each of the following functions with respect to x : (i)...

    Text Solution

    |

  11. Differentiate the following function with respect to x : sin^(-1)(si...

    Text Solution

    |

  12. Differentiate sin^(-1)(2xsqrt(1-x^2))w i t hr e s p e c ttox ,if -1/(...

    Text Solution

    |

  13. Differentiate sin^(-1)(3x-4x^3)

    Text Solution

    |

  14. Differentiate cos^(-1)(2x^2-1) with respect to x , if 0<x<1 (ii) -1<x...

    Text Solution

    |

  15. If y=cos^(-1){xsqrt(1-x)+sqrt(x)sqrt(1-x^2)} and 0<x<1 find (dy)/(dx)

    Text Solution

    |

  16. If y=sqrt(a^2-x^2) , prove that y(dy)/(dx)+x=0

    Text Solution

    |

  17. If y=e^x+e^(-x),"p r o v et h a t"(dy)/(dx)=sqrt(y^2-4)

    Text Solution

    |

  18. If y=sqrt(x^2+a^2) ,prove that y(dy)/(dx)-x=0

    Text Solution

    |

  19. If y=xsin^(-1)x+sqrt(1-x^2), p rov et h a t(dy)/(dx)=sin^(-1)x

    Text Solution

    |

  20. If y=1/2log((1-cos2x)/(1+cos2x)),p rov et h a t(dy)/(dx)=2cos e c2x

    Text Solution

    |