Home
Class 12
MATHS
If sin (x + y) = y cos (x + y) then prov...

If sin (x + y) = y cos (x + y) then prove that
`dy/dx =-(1 + y^2)/y^2`

Promotional Banner

Topper's Solved these Questions

  • AREA UNDER PLANE CURVES

    MODERN PUBLICATION|Exercise PROBLEM|2 Videos

  • DETERMINANTS

    MODERN PUBLICATION|Exercise PROBLEM|44 Videos

Similar Questions

Explore conceptually related problems

If cos y = x cos(a+y) then prove that dy/dx = (cos^2(a+y))/sin a

If e^(x) + e^(y) = e^(x + y) , then prove that (dy)/(dx) = (e^(x)(e^(y) - 1))/(e^(y)(e^(x) - 1)) or (dy)/(dx) + e^(y - x) = 0 .

If y=(x)/(x+2) then prove that x(dy)/(dx)=(1-y)y .

If xy log(x + y) = 1 , then prove that (dy)/(dx) = -(y(x^(2)y + x + y))/(x(xy^(2) + x + y)) .

If y = a sinx + b cos x then prove that y^2 + ((dy)/(dx))^2 = a^2 + b^2 .

If x^y = e^(x-y) then prove that (dy)/(dx)=logx/(1+logx)^2 .

If sin y = x sin (a + y) then show that (dy)/(dx)=(sin^2(a+y))/(sina)

MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-PROBLEM
  1. If e^(x)+e^(y)=e(x+y) find dy/dx.

    Text Solution

    |

  2. Differntiate the following functions by proper substitution. [((1+t^2)...

    Text Solution

    |

  3. If sin (x + y) = y cos (x + y) then prove that dy/dx =-(1 + y^2)/y^2

    Text Solution

    |

  4. Find dy/dx if log sqrt(x^2+y^2)=tan^(-1) (y/x)

    Text Solution

    |

  5. sinx=2t/1+t^(2), tany=2t/1-t^(2), find dy/dx.

    Text Solution

    |

  6. Find dy/dx, x=3 cos t-2cos^3t, y=3sint-2sin^3t.

    Text Solution

    |

  7. If y=sin(mcos^(-1)x) then prove that (1-x^(2))y(2)-xy(1)+m^(2)y=0.

    Text Solution

    |

  8. If y=cos^(-1)((2cosx-3sinx)/sqrt13), then find dy/dx.

    Text Solution

    |

  9. Examine the continuity of the following functions at indicated points....

    Text Solution

    |

  10. Show that f(x)={(x sin frac{1}{x}, xne0),(o,x=0):} is continuous at x...

    Text Solution

    |

  11. Prove that e^x-2=0 has a solution between 0 and 1.

    Text Solution

    |

  12. So that x^5+x+1=0 for some value of x between -1 and 0.

    Text Solution

    |

  13. Examine continuity and differentiability f(x)={[(1-e^(-x))/x,x!=0],[1,...

    Text Solution

    |

  14. If x=2costheta-cos2theta , y= 2sintheta-sin2theta then find d^(2)y/dx^...

    Text Solution

    |

  15. If y =(sin^(-1) x)^2, prove that (1-x^2)y2 - xy1 - 2 = 0

    Text Solution

    |

  16. Find dy/dx for the following . y=log(2)sqrtsinphi(x).

    Text Solution

    |

  17. Find dy/dx if (x/a)^(2/3) + (y/b)^(2/3) = 1

    Text Solution

    |

  18. Find dy/dx if y = x cot^(-1) (x/y)

    Text Solution

    |

  19. Find dy/dx if (cosx)^(y)=(siny)^(x)

    Text Solution

    |

  20. Find (dy)/(dx), if y=tan^(-1)((cosx)/(1+sinx)).

    Text Solution

    |