Home
Class 12
MATHS
Find (dy)/(dx) when : y="sin"^(-1) (1...

Find `(dy)/(dx)` when :
`y="sin"^(-1) (1)/(sqrt(1+x^(2)))+tan^(-1) ( (sqrt(1+x^(2))-1)/(x))`

Text Solution

Verified by Experts

The correct Answer is:
`-(1)/(2(1+x^(2)))`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CHHAYA PUBLICATION|Exercise EXERCISE 3B (Multiple Choice Type Questions)|9 Videos

  • DIFFERENTIATION

    CHHAYA PUBLICATION|Exercise EXERCISE 3B (Very Short Answer Type Questions)|33 Videos

  • DIFFERENTIATION

    CHHAYA PUBLICATION|Exercise EXERCISE 3A ( Short Answer Type Questions)|72 Videos

  • DIFFERENTIAL EQUATIONS OF THE FIRST ORDER AND FIRST DEGREE

    CHHAYA PUBLICATION|Exercise E ASSERTION-REASON TYPE|2 Videos

  • DIRECTION COSINES AND DIRECTION RATIOS

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos

Similar Questions

Explore conceptually related problems

Find (dy)/(dx) , when y="tan"^(-1)(x)/(1+sqrt(1-x^(2)))+sin(2 tan^(-1)sqrt((1-x)/(1+x)))

Find (dy)/(dx) when : y=sin[2 tan^(-1) sqrt((1-x)/(1+x))]

Find (dy)/(dx) when : y= 2 tan^(-1) sqrt((x-a)/(b-x))

Find int(sin^(-1)x)/(sqrt(1-x^(2)))dx

Find (dy)/(dx) in the following : y= sin^(-1) (2x sqrt(1-x^(2))), (-1)/(sqrt(2)) lt x lt (1)/(sqrt(2)) .

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

Find (dy)/(dx) when : y= tan^(-1)[sqrt((a-b)/(a+b))"tan"(x)/(2)]

Find (dy)/(dx) , when y="tan"^(-1)(sqrt(x)-4sqrt(x))/(1+4sqrt(x^(3)))

Find (dy)/(dx)," if "y= sin^(-1)x +sin^(-1)sqrt(1-x^(2)), 0 lt x lt 1 .

Find (dy)/(dx) if y=sec^(-1)((sqrt(x)+1)/(sqrt(x)-1))+sin^(-1)((sqrt(x)-1)/(sqrt(x)+1))

CHHAYA PUBLICATION-DIFFERENTIATION-EXERCISE 3A ( Long Answer Type Questions)
  1. Find (dy)/(dx) when : y= tan^(-1)[sqrt((a-b)/(a+b))"tan"(x)/(2)]

    Text Solution

    |

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

    Text Solution

    |

  3. Find (dy)/(dx) when : y="sin"^(-1) (1)/(sqrt(1+x^(2)))+tan^(-1) ( (...

    Text Solution

    |

  4. Find (dy)/(dx) when : x^(sin y)+y^(sinx)=1

    Text Solution

    |

  5. If y=[(tan x)^(tan x)]^(tan x)," find " (dy)/(dx)" at " x=(pi)/(4).

    Text Solution

    |

  6. If y=(1+sin theta+cos theta)/(1+sin theta-cos theta)," show that, " (...

    Text Solution

    |

  7. If tan y=(tan x+sec x-1)/(tan x-sec x+1), " show that, " (dy)/(dx)=(1...

    Text Solution

    |

  8. If y= tan^(-1)((a cos x-b sin x)/(b cos x+a sin x))" show that, " (dy...

    Text Solution

    |

  9. If cosy=x cos(a+y)," prove that " (dy)/(dx) =(cos^(2)(a+y))/(sin a), ...

    Text Solution

    |

  10. If y^(x)=e^(y-x)" prove that, " (dy)/(dx)=((logey)^(2))/(log y).

    Text Solution

    |

  11. If y= (x)/(2) sqrt(x^(2)-a^(2))-(a^(2))/(2) log (x+sqrt(x^(2)-a^(2)))...

    Text Solution

    |

  12. If y= 2"sin"^(-1)(x-2)/(sqrt(6))-sqrt(2+4x-x^(2)), show that (dy)/(dx...

    Text Solution

    |

  13. If f(x)=((a+x)/(1+x))^(a+1+2x), show that f'(0) =a^(a+1)[2log a+(1-a^...

    Text Solution

    |

  14. If f(x)=((a+x)/(b+x))^(x)+cosx find f'(0).

    Text Solution

    |

  15. If y=tan^(-1) [(sqrt(1+t^(2))+sqrt(1-t^(2)))/(sqrt(1+t^(2))-sqrt(1-t^...

    Text Solution

    |

  16. If y="cot"^(-1) (sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)), show tha...

    Text Solution

    |

  17. If (1+x)^(n)=^(n)C(0)+^(n)C(1)x+^(n)C(2)x^(2)+…+^(n)C(n)x^(n), prove t...

    Text Solution

    |

  18. If (1+x)^(n)=^(n)C(0)+^(n)C(1)x+^(n)C(2)x^(2)+…+^(n)C(n)x^(n), prove t...

    Text Solution

    |

  19. If siny=x sin(a+y), prove that, (dy)/(dx)=(sin a)/(1-2x cos a +x^(2)).

    Text Solution

    |

  20. If y=|(f(x),g(x),h(x)),(l,m,n),(a, b,c)|, prove that, (dy)/(dx)=|(f'(x...

    Text Solution

    |