Home
Class 12
MATHS
If xsqrt(1+y) + ysqrt(1+x) = 0 for x lie...

If `xsqrt(1+y) + ysqrt(1+x) = 0` for x lies between -1 and 1` prove that dy/dx =-1/(1+x)^2

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    PSEB|Exercise Exercise|151 Videos

  • APPLICATION OF DERIVATIVES

    PSEB|Exercise Exercise|189 Videos

  • DETERMINANTS

    PSEB|Exercise Exercise|101 Videos

Similar Questions

Explore conceptually related problems

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

If xy = e^(x-y) , prove that dy/dx = (y(x-1))/(x(y+1))

If xsqrt(1 + y) + ysqrt(1 + x) = 0 show that (dy)/(dx) = - 1/(1 + x)^2

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

If sqrt(1 - x^6) + sqrt(1 - y^6) = a^3 (x^3 - y^3) prove that (dy)/(dx) = (x^2 sqrt(1 - y^6))/(y^2 sqrt(1 - x^6))

If y = (x sin^(-1) x)/(sqrt(1 - x^2)) + "log" sqrt(1 - x^2) , prove that (dy)/(dx) = (sin^(-1)x)/((1 - x^2)^(3//2))

If xy = e^(x - y) , prove that (dy)/(dx) = (y (x - 1))/(x (y + 1))

If y = sin^(-1) x^2 sqrt(1 - x^2) + xsqrt(1 - x^4) , show that (dy)/(dx) - (2x)/(sqrt(1 - x^4)) = 1/(sqrt(1 - x^2))

If y = tan^-1 (4x)/(1+5x^2) + tan^-1(2+3x)/(3-2x) , prove that dy/dx = 5/(1+25x^2)

PSEB-CONTINUITY AND DIFFERENTIABILITY-Exercise
  1. Differentiate w.r.t. x the function : sin^-1(xsqrtx), 0lexle1

    Text Solution

    |

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

    Text Solution

    |

  3. Differentiate w.r.t. x the function : cot^-1[(sqrt(1+sinx) + sqrt(1-si...

    Text Solution

    |

  4. Differentiate w.r.t. x the function : (logx)^logx, x>1

    Text Solution

    |

  5. Differentiate w.r.t. x the function : cos(acosx+bsinx), for some const...

    Text Solution

    |

  6. Differentiate w.r.t. x the function : (sinx - cosx)^(sinx-cosx), x lie...

    Text Solution

    |

  7. Differentiate w.r.t. x the function : x^x + x^a + a^x + a^a, for some ...

    Text Solution

    |

  8. Differentiate w.r.t. x the function : x^(x^2-3) + (x-3)^(x^2), for x>...

    Text Solution

    |

  9. Find dy/dx if y =12(1-cost), x =10(t-sint)

    Text Solution

    |

  10. Find dy/dx if y = sin^-1x + sin^-1 sqrt(1-x^2), 0ltxlt1

    Text Solution

    |

  11. If xsqrt(1+y) + ysqrt(1+x) = 0 for x lies between -1 and 1 prove that ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. If f(x) = |x|^3 show that f''(x) exists for all real x and find it.

    Text Solution

    |

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

    Text Solution

    |

  17. Using the fact that sin(A+B) = sinA cosB + cosA sinB and the differen...

    Text Solution

    |

  18. Does there exist a function which is continuous everywhere but not dif...

    Text Solution

    |

  19. If y = |[f(x),g(x),h(x)],[1,m,n],[a,b,c]|, prove that dy/dx = |[f'(x)...

    Text Solution

    |

  20. If y = e^(acos^-1x), -1lexle1, show that (1-x^2)(d^2y)/dx^2 - x(dy/dx)...

    Text Solution

    |