Home
Class 12
MATHS
If cos^(-1)((x^2-y^2)/(x^2+y^2))=tan^(-1...

If `cos^(-1)((x^2-y^2)/(x^2+y^2))=tan^(-1)a ,` prove that `(dy)/(dx)=y/xdot`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIALS, ERRORS AND APPROXIMATIONS

    RD SHARMA ENGLISH|Exercise All Questions|107 Videos

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA ENGLISH|Exercise All Questions|90 Videos

Similar Questions

Explore conceptually related problems

If tan^(-1)((x^2-y^2)/(x^2+y^2))=a , prove that (dy)/(dx)=x/y((1-tana))/((1+tana)) .

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

If log ((x^(2) -y^(2))/( x^(2)+ y^(2))) =a, Prove that (dy)/(dx) =(y)/(x).

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

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

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

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

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

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

RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. If y = cos^(-1)(2x)+2cos^(-1)sqrt(1-4x^2), -1/2ltxlt0 , find (dy)/(dx...

    Text Solution

    |

  2. If sqrt(1-x^6)+sqrt(1-y^6)=a(x^3-y^3),p rov et h a t(dy)/(dx)=(x^2)/(y...

    Text Solution

    |

  3. If cos^(-1)((x^2-y^2)/(x^2+y^2))=tan^(-1)a , prove that (dy)/(dx)=y/xd...

    Text Solution

    |

  4. Differentiate cos^(-1)(2x^2-1) with respect to x , if 0<x<1 (ii) -1<x...

    Text Solution

    |

  5. Differentiate tan^(-1)((3x-x^3)/(1-3x^2)) , if -1/(sqrt(3))<x<1/(sqrt(...

    Text Solution

    |

  6. Differentiate each of the following functions with respect to x : (...

    Text Solution

    |

  7. Differentiate the following function with respect to x : sin^(-1)(si...

    Text Solution

    |

  8. Differentiate sin^(-1)(2xsqrt(1-x^2))w i t hr e s p e c ttox ,if -1/(...

    Text Solution

    |

  9. Differentiate sin^(-1)(3x-4x^3) with respect to x , if (i)-1/2ltxlt...

    Text Solution

    |

  10. Differentiate cos^(-1)(2x^2-1) with respect to x , if 0<x<1 (ii) -1<x...

    Text Solution

    |

  11. If y=cos^(-1){xsqrt(1-x)+sqrt(x)sqrt(1-x^2)} and 0<x<1, find (dy)/(dx...

    Text Solution

    |

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

    Text Solution

    |

  13. If y=e^x+e^(-x),"p r o v et h a t"(dy)/(dx)=sqrt(y^2-4)

    Text Solution

    |

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

    Text Solution

    |

  15. If y=xsin^(-1)x+sqrt(1-x^2), p rov et h a t(dy)/(dx)=sin^(-1)x

    Text Solution

    |

  16. If y=1/2log((1-cos2x)/(1+cos2x)),p rov et h a t(dy)/(dx)=2cos e c2x

    Text Solution

    |

  17. If y=x e^x, find dy/dx

    Text Solution

    |

  18. If 'y=(x-1)log(x-1)-(x+1)log(x+1),p rov et h a t(dy)/(dx)=log((x-1)/(...

    Text Solution

    |

  19. If y=sqrt(x)+1/(sqrt(x)),p rov et h a t2x(dy)/(dx)=sqrt(x)-1/(sqrt(x))

    Text Solution

    |

  20. P rov et h a t d/(dx){x/2sqrt(a^2-x^2)+(a^2)/2sin^(-1)(x/a) }=sqrt(a^2...

    Text Solution

    |