Home
Class 11
MATHS
If log(x^2+y^2)=2tan^(-1)(y/x), show th...

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

Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

  • LINEAR INEQUALITIES

    CENGAGE PUBLICATION|Exercise All Questions|68 Videos

Similar Questions

Explore conceptually related problems

(dy)/(dx)=tan^(2)(x+y)

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

(dy)/(dx)=(y)/(x)-tan""(y)/(x)

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

If y=e^(x^(e ^(x^(...oo)))) ,show that, (dy)/(dx)=(y^(2)logy)/(x(1-y log x logy)) .

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

If x="tan"(y)/(2)+"log tan"(y)/(2)-2log(1+"tan"(y)/(2)) , show that, (dy)/(dx)=(1)/(2)"sin"(1+sin y+cos y)

If y=a^(x^(a^(x^(…oo)))) , show that, (dy)/(dx)=(y^(2)logy)/(x(1-y log x log y)) .

If x=y^(y^(y^(...oo))) , then show that, (dy)/(dx)=(y(1-x logy))/(x^(2)) .

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

CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. If x^3+y^3+3a x y=0 , f i n d dy / dx

    Text Solution

    |

  2. If 1 is the twice repeated root of the equation a x^3+b x^2+b x+d=0,t ...

    Text Solution

    |

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

    Text Solution

    |

  4. If y=btan^(-1)(x/a+tan^(-1)y/x),find(dy)/(dx)dot

    Text Solution

    |

  5. Let y=sqrt(x+sqrt(x+sqrt(x+oo))) , (dy)/(dx) is equal to (a)1/(2y-...

    Text Solution

    |

  6. If y=sqrt(sinx+y), then find (dy)/(dx)

    Text Solution

    |

  7. f(x)=|x^2-3|x|+2|dot Then which of the following is/are true f^(prime)...

    Text Solution

    |

  8. If xsqrt(1+y)+ysqrt(1+x)=0, prove that dy/dx=(-1)/((1+x)^2

    Text Solution

    |

  9. If x^3-2x^2y^2+5x+y-5=0 and y(1)=1, then (a)y^(prime)(1)=4/3 (b) y...

    Text Solution

    |

  10. If x^y=e^(x-y), Prove that dy/dx=logx/(1+logx)^2

    Text Solution

    |

  11. Let f(x)=(sqrt(x-2sqrt(x-1)))/(sqrt(x-1)-1)xdot Then (a)f^(prime)(10...

    Text Solution

    |

  12. If sqrt(x) +sqrt(y)=4, f i n d (dx/dy) a t (y = 1).

    Text Solution

    |

  13. If y=(x^4-x^2+1)/(x^2+sqrt(3)x+1) and (dy)/(dx)=a x+b , then the value...

    Text Solution

    |

  14. If x y+y^2=tanx+y ,then find (dy)/(dx)

    Text Solution

    |

  15. Find (dy)/(dx) for y=sin^(-1)(cosx)

    Text Solution

    |

  16. If y=sqrt(x+sqrt(y+sqrt(x+sqrty+...oo))) then (dy)/(dx) equal to

    Text Solution

    |

  17. If y=x^(logx)^(("log"(logdotx))),t h e n(dy)/(dx)i s y/x(1n x^(oox-1)...

    Text Solution

    |

  18. If y=sqrt(sinx+sqrt(sinx+sqrt(sinx+ tooo))) ,prove that (dy)/(dx)=(cos...

    Text Solution

    |

  19. The n t h derivative of x e^x vanishes when (a)x=0 (b) x=-1 (c)...

    Text Solution

    |

  20. If x=a(cost+1/2logtan^2t) and y=asint then find (dy)/(dx) at t=pi/4

    Text Solution

    |