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

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

Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DERIVATIVES

    SHARAM PUBLICATION|Exercise EXAMPLE|118 Videos

  • DETERMINANT

    SHARAM PUBLICATION|Exercise EXAMPLE|90 Videos

Similar Questions

Explore conceptually related problems

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

If x=alphasin2t(1+cos2t) and y=betacos 2t(1-cos2t) , then show that (dy)/(dx)=(beta)/(alpha)tan t .

If y=(sin^(-1)x)/(sqrt(1-x^(2))) , the prove that (1-x^(2))(d^(2)y)/(dx^(2))-3x(dy)/(dx)-y=0 .

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

If x=asin2t(1+cos2t) and y=bcos2t(1-cos2t) , then show that at t=(pi)/(4),(dy)/(dx)=(b)/(a)

If y=x sin^(-1)x +x cos^(-1)x , then whtat is (dy)/(dx) ?

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

If y=sqrt((1-sin2x)/(1+sin2x)) , then show that (dy)/(dx)+sec^(2)((pi)/(4)-x)=0,x in [0,(pi)/(4)]

SHARAM PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXAMPLE
  1. If e^(y//x)=(x)/(a+bx) then show that x^(3)(d)/(dx)((dy)/(dx))=(x(dy)/...

    Text Solution

    |

  2. If (cosx)^(y)=(cosy)^(x), then find (dy)/(dx).

    Text Solution

    |

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

    Text Solution

    |

  4. Differentiate tan^(-1)((sqrt(1+x^2)-1)/x) w.r.t x.

    Text Solution

    |

  5. If y=(tan^(-1)x)^2 then show that (x^2+1)^2 (d^2y)/(dx^2)+2x(x^2+1)((d...

    Text Solution

    |

  6. If y=x^(sinx-cosx)+(x^(2)-1)/(x^(2)+1), then find (dy)/(dx)

    Text Solution

    |

  7. If x=a(cost+tsint) and y=a(sint-tcost), then find (d^(2)y)/(dx^(2)) at...

    Text Solution

    |

  8. If x= cos t+ log tan t/2 and y = sin t, then find the value of (d^2y)/...

    Text Solution

    |

  9. If xsqrt(1+y)+ysqrt(1+x)=0 for -1ltx,ylt1 then prove that (dy)/(dx)=(-...

    Text Solution

    |

  10. If x=tan(1/a logy), show that (1+x^2)d^2y/dx^2+(2x-a)dy/dx=0.

    Text Solution

    |

  11. Differentiate the following function w.r.tx tan^(-1)((sqrt(1+x)-sqrt(1...

    Text Solution

    |

  12. If y=sin^(-1)[((5x+12(sqrt(1-x^2)))/13)] then find (dy)/(dx).

    Text Solution

    |

  13. If y=tan(x+y), then find (dy)/(dx).

    Text Solution

    |

  14. If y=x^(cotx)+(sinx)^x then find (dy)/(dx).

    Text Solution

    |

  15. If y=(sin^(-1)x)/(sqrt(1-x^(2))), the prove that (1-x^(2))(d^(2)y)/(dx...

    Text Solution

    |

  16. If x = (1-cos^2 theta)/(cos theta), y = (1-cos^(2n)theta)/(cos^n theta...

    Text Solution

    |

  17. If y=(log x)^(cos x)+(x^2+1)/(x^2-1) find (dy)/(dx).

    Text Solution

    |

  18. If y= cos^(-1)[(3x+4sqrt(1-x^2))/5] then find (dy)/(dx).

    Text Solution

    |

  19. Prove that cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-...

    Text Solution

    |

  20. Differentiate sin^(-1) (2ax sqrt(1-a^2x^2)) wth respect to sqrt(1-a^2...

    Text Solution

    |