Home
Class 12
MATHS
Differentiate sin^(-1)((2x)/(1+x^2)) wit...

Differentiate `sin^(-1)((2x)/(1+x^2))` with respect to `x` , when `x in (-1,\ 1)`

Text Solution

Verified by Experts

given that,
`y=sin^(-1)((2x)/(1+x^2))`
`x in (-1,\ 1)`
`x=tan theta `
so, `y= sin^-1[(2tan theta)/(1+tan^2 theta )]`
`=>y=sin^-1 (sin 2theta )`
`x in (-1,\ 1)`
`=>theta in (-pi/4,pi/4)`
`=>2 theta in (-pi/2,pi/2)`
`y=sin^-1 (sin 2theta )`
`=>y=2 theta`
`=>y=2 tan^-1 x`
`(dy)/(dx)= 2*d/(dx)(tan^-1x)`
`=2/(1+x^2)`
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

Differentiate sin^(-1)((2x)/(1+x^(2))) with respect to x, when x in(1,oo)

Differentiate sin^(-1)((2x)/(1+x^(2))) with respect to x, when x in(-oo,-1)

Differentiate sin^(-1)((2^(x+1))/(1+4^(x))) with respect to x

Differentiate sin((1+x^(2))/(1-x^(2))) with respect to x

Differentiate sin^(-1)((1)/(sqrt(1+x^(2)))) with respect to x

Differentiate sin ^(-1) (1/sqrt(1+x^2)) with respect to 'x'

Differentiate sin^(-1)(2x sqrt(1-x^(2))) with respect to x, if '-1

Differentiate (a^(sin^(-1)x))^(2) with respect to x:

Differentiate sin^(-1)(3x-4x^(3)) with respect to x, if '-1/2

Differentiate sin^(-1)(3x-4x^(3)) with respect to x, if '1/2

RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. Differentiate tan^(-1)((3x-x^3)/(1-3x^2)) , if x >1/(sqrt(3))

    Text Solution

    |

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

    Text Solution

    |

  3. Differentiate sin^(-1)((2x)/(1+x^2)) with respect to x , when x in (-1...

    Text Solution

    |

  4. Differentiate sin^(-1)((2x)/(1+x^2)) with respect to x , when x in (1,...

    Text Solution

    |

  5. Differentiate sin^(-1)((2x)/(1+x^2)) with respect to x , when x in (-o...

    Text Solution

    |

  6. Differentiate cos^(-1)((1-x^2)/(1+x^2)) with respect to x , when x in ...

    Text Solution

    |

  7. Differentiate cos^(-1)((1-x^2)/(1+x^2)) with respect to x , when x in ...

    Text Solution

    |

  8. Differentiate cos^(-1)((1-x^2)/(1+x^2)), 0lt xlt1 with respect to x

    Text Solution

    |

  9. Differentiate sin^(-1)((1-x^2)/(1+x^2)), 0ltxlt1 with respect to x

    Text Solution

    |

  10. Differentiate cos^(-1)((2x)/(1+x^2)) , -1ltxlt1 with respect tox

    Text Solution

    |

  11. Differentiate sec^(-1)(1/(2x^2-1)), 0ltxlt1/(sqrt(2)) with respect to ...

    Text Solution

    |

  12. Differentiate sin^(-1)(2xsqrt(1-x^2)),-1/(sqrt(2))ltxlt1/(sqrt(2)) wit...

    Text Solution

    |

  13. Differentiate cos^(-1)(2xsqrt(1-x^2)) , -1/(sqrt(2)) lt x lt 1/sqrt2

    Text Solution

    |

  14. Differentiate tan^(-1){(1-cosx)/(sinx)},-piltxltpi with respect to x :

    Text Solution

    |

  15. Differentiate tan^(-1){sqrt((1-cosx)/(1+cosx))}, -piltxltpi with respe...

    Text Solution

    |

  16. Differentiate tan^(-1){sqrt((1+cosx)/(1-cosx))},0<x<pi with respect to...

    Text Solution

    |

  17. Differentiate tan^(-1){(cosx)/(1+sinx)},0ltxltpi

    Text Solution

    |

  18. Differentiate tan^(-1){sqrt((1+sinx)/(1-sinx))}, -pi/2ltxltpi/2 with r...

    Text Solution

    |

  19. Differentiate tan^(-1)(secx+tanx) , -pi/2ltxltpi/2 with respect to x :

    Text Solution

    |

  20. Differentiate tan^(-1){sqrt(1+x^2)+x},\ x in RR with respect to x .

    Text Solution

    |