Home
Class 11
MATHS
y=sin^(-1)(xsqrt(1-x)+sqrtxsqrt(1-x^2)) ...

`y=sin^(-1)(xsqrt(1-x)+sqrtxsqrt(1-x^2))` show that `dy/dx=(1)/(sqrt(1-x^2))-1/(2(sqrt(x-x^2)))`

Promotional Banner

Topper's Solved these Questions

  • CONIC SECTION

    PATHFINDER|Exercise QUESTION BANK|25 Videos

  • FUNCTION

    PATHFINDER|Exercise QUESTION BANK|296 Videos

Similar Questions

Explore conceptually related problems

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

If y = sin^(-1){(5x+12sqrt(1-x^2))/13} then show that (dy)/(dx) = 1/sqrt(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 sqrt(1-x^4)+sqrt(1-y^4)=k(x^2-y^2) ,show that y_1=(xsqrt(1-y^4))/(ysqrt(1-x^4))

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

If y="cot"^(-1) (sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)) , show that [(dy)/(dx)]_(x=(1)/(2))= -(1)/(sqrt(3)) .

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

d/(dx)[cos^(-1)(xsqrt(x)-sqrt((1-x)(1-x^2)))]= 1/(sqrt(1-x^2))-1/(2sqrt(x-x^2)) (-1)/(sqrt(1-x^2))-1/(2sqrt(x-x^2)) 1/(sqrt(1-x^2))+1/(2sqrt(x-x^2)) 1/(sqrt(1-x^2)) 0 b. 1//4 c. -1//4 d. none of these

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

PATHFINDER-DERIVATIVES-QUESTION BANK
  1. y=x^(x^(x^------infty) then prove that dy/dx=(y^2)/(x(1-ylogx))

    Text Solution

    |

  2. If y=tan^(-1)(5ax)/(a^2-6x^2) prove that dy/dx=(3a)/(a^2+9x^2)+(2a)/(a...

    Text Solution

    |

  3. y=sin^(-1)(xsqrt(1-x)+sqrtxsqrt(1-x^2)) show that dy/dx=(1)/(sqrt(1-x^...

    Text Solution

    |

  4. f(x) is differentiable at x=a prove that underset(xrarra)Lt ((x+a)f(a)...

    Text Solution

    |

  5. If y=g{g(x)}, g(0)=0 and g'(0)=2 then find dy/dx at x=0

    Text Solution

    |

  6. 2f(x)+3f(-x)=x^2-x+1 then determine f'(1)

    Text Solution

    |

  7. x=sectheta-costheta , y=sec^n theta- cos^n theta show that (dy/dx)^2=(...

    Text Solution

    |

  8. y=tan^(-1) ((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)) show that dy/d...

    Text Solution

    |

  9. f(x)=5x-4 (0ltxle1) =4x^2-3x (1ltxlt2) test whether f(x) is differenti...

    Text Solution

    |

  10. find the derivative of x^x

    Text Solution

    |

  11. Find by the defination the differential coefficient of the following: ...

    Text Solution

    |

  12. Find derivative of the following: sec3x

    Text Solution

    |

  13. Find derivative of the following:e^(sqrtx)

    Text Solution

    |

  14. Find derivative of the following: sin^(-1)x

    Text Solution

    |

  15. Find by the definition the differential coefficient of the following: ...

    Text Solution

    |

  16. Find by the definition the differential coefficient of the following:l...

    Text Solution

    |

  17. Find by the definition the differential coefficient of the following: ...

    Text Solution

    |

  18. Find by the definition the differential coefficient of the following: ...

    Text Solution

    |

  19. Find by the definition the differential coefficient of the following: ...

    Text Solution

    |

  20. Find by the definition the differential coefficient of the following: ...

    Text Solution

    |