Home
Class 12
MATHS
If x^4+y^4-a^2xy=0 " then find " dy/dx...

If `x^4+y^4-a^2xy=0 " then find " dy/dx`

A

`dy/dx =(a^2-4x^3)/(4y^3-a^2x)`

B

`dy/dx =(a^2y-x^3)/(4y^3-a^2x)`

C

`dy/dx =(a^2y-4x^3)/(y^3-a^2x)`

D

`dy/dx =(a^2y-4x^3)/(4y^3-a^2x)`

Text Solution

Verified by Experts

The correct Answer is:
D
`x^4+y^4-a^2xy=0 `
`4x^3+4y^3 dy/dx`
`4x^3+4y^3 dy/dx-a^2(xdy/dx+y.1)=0`
`rArr 4x^3 +3y^3dy/dx-a^2xdy/dxa^2y=0`
`rArr dy/dx(4y^3-a^3x)=a^2y-4x^3`
`rArr dy/dx =(a^2y-4x^3)/(4y^3-a^2x)`
Promotional Banner

Topper's Solved these Questions

  • Continuity and Differentiability

    NAGEEN PRAKASHAN|Exercise Exercies 5a|30 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN|Exercise Exercies 5b|7 Videos

  • APPLICATIONS OF INTEGRALS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|19 Videos

  • DETERMINANTS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

"If "xy=e^((x-y))," then find "(dy)/(dx).

If x^(4) + y^(4) = 3xy, "then " (dy)/(dx) is equal to

If xy+y^(2)=tan x+y, then find (dy)/(dx)

"If "xy+y^(2)=tan x + y," then find "(dy)/(dx).

If 3x^(2)+4xy-5y^(2)=0," then: "(dy)/(dx)=

If sec (x+y) = xy, then find (dy)/(dx)

xy=(x+y)^(2) then find (dy)/(dx)

y^(2)+xy=tan(x+y) then find (dy)/(dx)=?

If xy=e^((x-y)), then find (dy)/(dx)

If y^(5)+xy^(2)+x^(3)=4x+3, then find (dy)/(dx) at (2 1)

NAGEEN PRAKASHAN-Continuity and Differentiability-Miscellaneous Exercise
  1. If x^4+y^4-a^2xy=0 " then find " dy/dx

    Text Solution

    |

  2. Differentiate w.r.t. x the function. (3x^2-9x+5)^9

    Text Solution

    |

  3. Differentiate w.r.t. x the functionsin^3x+cos^6x

    Text Solution

    |

  4. Find dy/dx if y= (5x)^(3cos 2x)

    Text Solution

    |

  5. sin^(-1)(xsqrt(x)),0 le x le 1

    Text Solution

    |

  6. Differentiate w.r.t. x the function (cos^(-1)x/2)/(sqrt(2x+7)),-2<x<2

    Text Solution

    |

  7. cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=(x)/...

    Text Solution

    |

  8. (log x)^(log x),x gt1

    Text Solution

    |

  9. Differentiate w.r.t. x the function cos" "(a" "cos" "x" "+" "b" "s in"...

    Text Solution

    |

  10. (sinx-cosx)^((sinx-cosx)),(pi)/(4) ltx lt (3pi)/(4)

    Text Solution

    |

  11. Differentiate w.r.t. x the function x^x+x^a+a^x+a^a ,for some fixed a...

    Text Solution

    |

  12. Differentiate x^x^(2-3)+(x-3)^x^2 with respect to x :

    Text Solution

    |

  13. Find (dy)/(dx),if y=12(1-cost), x=10(t-sint),-pi/2<t<pi/2

    Text Solution

    |

  14. If y=sin^(- 1)x+sin^(- 1)sqrt(1-x^2) then find (dy)/(dx)

    Text Solution

    |

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

    Text Solution

    |

  16. If (x-a)^2+(y-b)^2=c^2, for some c > 0, prove that ([1+((dy)/(dx))^2]^...

    Text Solution

    |

  17. If cosy=xcos(a+y), with cosa!=+-1, prove that (dy)/(dx)=(cos^2(a+y...

    Text Solution

    |

  18. If x=a(cost+tsint) and y=a(sint-tcost), find (d^(2)y)/(dx^(2)).

    Text Solution

    |

  19. If f(x)=|x|^3 , show that f"(x) exists for all real x and find it.

    Text Solution

    |

  20. Using mathematical induction prove that d/(dx)(x^n)=n x^(n-1) for all...

    Text Solution

    |

  21. Using the fact that s in (A + B) = s in A cos B + cos A s in Band the ...

    Text Solution

    |