Home
Class 12
MATHS
If x= sqrta^(sin^-1t), y = sqrt(a^(cos^-...

If `x= sqrta^(sin^-1t), y = sqrt(a^(cos^-1t))`, show that `dy/dx = -y/x , a > 0`

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    PRADEEP PUBLICATION|Exercise EXERCISE|788 Videos

  • APPLICATIONS OF INTEGRALS

    PRADEEP PUBLICATION|Exercise EXERCISE|162 Videos

  • DETERMINANTS

    PRADEEP PUBLICATION|Exercise EXERCISE|342 Videos

Similar Questions

Explore conceptually related problems

Find dy/dx = -y/x if x = sqrt(a^(sin^-1t)), y = sqrt(a^(cos^-1t))

If sqrt(x^2 +1) y = log(sqrt(x^2+1)-x) , then show that (x^2 +1) dy/dx + xy + 1=0

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

If sqrt(1-x^2) + sqrt(1-y^2) = a(x-y), show that dy/dx = sqrt((1-y^2)/(1-x^2))

If y = sqrt((1+x)/(1-x)) , prove that (1-x^2) dy/dx - y = 0

If y = (sin^-1x)/(sqrt(1-x^2)) , prove that (1-x^2)(dy/dx)- xy = 1

If y = sin(2sin^-1x) , show that: dy/dx=2sqrt((1-y^2)/(1-x^2))

If x= e^(cos2t) and y = e^(sin2t) , then move that (dy)/(dx) = -(ylogx)/(xlogy) .

If y = sin^-1 x , show that : (1-x^2) d^2y/dx^2- x dy/dx=0

If x = (1 - t^2)/(1 + t^2) and y = (2t)/(1+t^2) , then show that (dy/dx) + x/y =0

PRADEEP PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Find dy/dx, if x and y are connected parametrically by the equations (...

    Text Solution

    |

  2. Find dy/dx, if x and y are connected parametrically by the equations (...

    Text Solution

    |

  3. If x= sqrta^(sin^-1t), y = sqrt(a^(cos^-1t)), show that dy/dx = -y/x ,...

    Text Solution

    |

  4. Find the second order derivatives of the function : x^2+3x+2

    Text Solution

    |

  5. Find the second order derivatives of the function: x^20

    Text Solution

    |

  6. Find the second order derivatives of the function : x cdot cosx

    Text Solution

    |

  7. Find the second order derivatives of the function : logx

    Text Solution

    |

  8. Find the second order derivatives of the function : x^3logx

    Text Solution

    |

  9. Find the second order derivatives of the function : e^x sin5x

    Text Solution

    |

  10. Find the second order derviatives of the functions : e^(2x) sin 3 x

    Text Solution

    |

  11. Find the second order derivatives of the function : tan^-1x

    Text Solution

    |

  12. Find the second order derivatives of the function : log(logx)

    Text Solution

    |

  13. Find the second order derivatives of the function : sin(logx)

    Text Solution

    |

  14. If y = 2 cos x -6 sin x, prove that (d^2y)/(dx^2)+y = 0

    Text Solution

    |

  15. Find the second order derivative of the following functions If y = c...

    Text Solution

    |

  16. If y = 3 cos (log x) + 4 sin (log x) show that x^2 y2 + xy1 + y = 0

    Text Solution

    |

  17. Find the second order derivative of the following functions If y = a...

    Text Solution

    |

  18. If y = 500e^7x + 600e^-7x show that (d^2y/dx^2) = 49y

    Text Solution

    |

  19. If e^y(x+1)=1 show that (d^2y/dx^2) = (dy/dx)^2 ਹੈ।

    Text Solution

    |

  20. If y=[tan^-1 x]^2, then prove that : (x^2 + 1)^2 y2+2x(x^2+1) y1 = 2.

    Text Solution

    |