Home
Class 12
MATHS
IF [log (x^2 + y^2) = 2 tan^-1 (y/x)] th...

IF `[log (x^2 + y^2) = 2 tan^-1 (y/x)]` then show that , dy/dx = (x+y) /(x- y)

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF INTEGRATION

    JMD PUBLICATION|Exercise EXAMPLE|7 Videos

  • Determinants

    JMD PUBLICATION|Exercise Exercise|20 Videos

Similar Questions

Explore conceptually related problems

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

If log (x^2+y^2)=2t a n^(-1)\ (y/x), then show that (dy)/(dx)=(x+y)/(x-y)

If y = log tan (pi/4+x/2) , show that: dy/dx-secx=0

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

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

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

If sin y = x sin (a+y), then show that: dy/dx=(sina)/(1-2xcosa+x^2)

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

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

JMD PUBLICATION-Continuity and differentiablity-Exercise
  1. IF [x= a {(1 + t^2) /(1-t^2)] and [y= 2t/(1 -t^2)] find dy/dx.

    Text Solution

    |

  2. If x= 3 sin t - sin 3t, y = 3 cos t - cos 3t, find d^2 y/dx^2 at t= pi...

    Text Solution

    |

  3. Differentiate [x ^(tan x) + sqrt(x^2 + 1 / x)] w.r.t X.

    Text Solution

    |

  4. IF y= x^x , show that [(d^2y/dx^2) -1/y(dy/dx)^2 - y/x = 0]

    Text Solution

    |

  5. x= a sin 2t(1 + cos2t) and y = b cos 2t(1- cos 2t) , show that [(dy/dx...

    Text Solution

    |

  6. Verify Lagrange's mean value theorem for the following function : [f(x...

    Text Solution

    |

  7. f(x) = [(1-sin^3x)/(3cos^2x) ,if x< pi/2], [a, if (x= pi/2) if f(x) b...

    Text Solution

    |

  8. IF [y{sqrt(x^2 + 1)- log {1/x +sqrt(1+1/x^2)}] find dy/dx

    Text Solution

    |

  9. IF y =[log (x+ sqrt(1+ x^2))]^2 ,show that (1+ x^2) (d^2y) /dx^2 +x(dy...

    Text Solution

    |

  10. Diff. [x^(sinx) + (sin x)^ cos x] w.r.t. x.

    Text Solution

    |

  11. IF [log (x^2 + y^2) = 2 tan^-1 (y/x)] then show that , dy/dx = (x+y) /...

    Text Solution

    |

  12. IF [y= (sin^-1) /sqrt(1-x^2)] show that : [(1 -x^2) (d^2y /dx^2) - 3x(...

    Text Solution

    |

  13. If y= e^(a sin^-1 x) , [-1le x le 1]then show that (1 -x^2) (d^2y) /(...

    Text Solution

    |

  14. IF [x^p y^q = (x+ y)^(p+q)], prove that dy/dx = y/x.

    Text Solution

    |

  15. Differentiate tan^-1{( sqrt (1+x^2) +sqrt (1-x^2))/ (sqrt(1+x^2)-sqrt(...

    Text Solution

    |

  16. If [(cos x)^y = (cos y)^x ] find dy/dx,

    Text Solution

    |

  17. Differentiate the following with respect to x: [ sin^-1 {2^(x+1) 3^x} ...

    Text Solution

    |

  18. IF [y= (tan^-1 x)^2 , show that [(x^2 +1)^2 d^2y/dx^2+2x (x^2 + 1)dy/d...

    Text Solution

    |

  19. Differentiate [tan^-1 {sqrt(1-x^2) /x}] with respect to [cos^-1 {2x ...

    Text Solution

    |

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

    Text Solution

    |