Home
Class 12
MATHS
If sqrt(y+x)+sqrt(y-x)=c ,show that ...

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

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 sqrt(y+x)+sqrt(y-x)=c ,s howt h a t(dy)/(dx)=y/x-sqrt((y^2)/(x^2)-1.)

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

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

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

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

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

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

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

sqrt(x+y)+sqrt(y-x)=c , then (d^2y)/(dx^2) equals

1. x(dy)/(dx)-y=x sqrt(x^(2)+y^(2))

RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. Differentiate the following functions with respect to (sin^(-1)x^4)...

    Text Solution

    |

  2. Find (dy)/(dx), y=((x^2-1)^3(2x-1))/(sqrt((x-3)(4x-1)))

    Text Solution

    |

  3. If sqrt(y+x)+sqrt(y-x)=c ,show that (dy)/(dx)=y/x-sqrt((y^2)/(x^2)...

    Text Solution

    |

  4. If (sinx)^y=(cosy)^x ,p rov et h a t(dy)/(dx)=(logcosy-ycotx)/(logsinx...

    Text Solution

    |

  5. If y=cos^(-1){(2x-3sqrt(1-x^2))/(sqrt(13))},"f i n d"(dy)/(dx)

    Text Solution

    |

  6. If e^x+e^y=e^(x+y),p rov e t h a t(dy)/(dx)+e^(y-x)=0

    Text Solution

    |

  7. If xsin(a+y)+sina cos(a+y)=0, prove that (dy)/(dx)=sin^2(a+y)/sina

    Text Solution

    |

  8. Find (dy)/(dx) in each of the following: (x^2+y^2)^2=x y

    Text Solution

    |

  9. Differentiate the following functions (2^xcosx)/((x^2+3)^2) with res...

    Text Solution

    |

  10. Differentiate the following functions with respect to e^sin^((-1...

    Text Solution

    |

  11. Differentiate the function "sin"(2sin^(-1)x) with respect to x.

    Text Solution

    |

  12. Differentiate the following function sqrt(tan^(-1)(x/2)) with respec...

    Text Solution

    |

  13. Differentiate the following function tan^(-1)(e^x) with respect to...

    Text Solution

    |

  14. Differentiate tan^(-1)((1+a x)/(1-a x)) with respect to sqrt(1+a...

    Text Solution

    |

  15. Differentiate tan^(-1)((x-1)/(x+1)) with respect to sin^(-1)(3x-4x...

    Text Solution

    |

  16. If y={log(cosx)sinx}"{"log(sinx)cosx")"^(-1)+sin^(-1)((2x)/(1+x^2)), ...

    Text Solution

    |

  17. If y=sec^(-1)((x+1)/(x-1))+sin^(-1)((x-1)/(x+1)),x > 0. Find (dy)/(dx)...

    Text Solution

    |

  18. Differentiate tan^(-1)(x/(sqrt(1-x^2))) with respect to sin^(...

    Text Solution

    |

  19. Differentiate sin^(-1)sqrt(1-x^2) with respect to cot^(-1)(x/sqrt(1...

    Text Solution

    |

  20. If ysqrt(x^2+1)=log(sqrt(x^2+)1-x),s howt h a t(x^2+1)(dy)/(dx)+x y+1=...

    Text Solution

    |