Home
Class 12
MATHS
If y=(x+sqrt(1+x^2))^n then (1+x^2)(d^...

If `y=(x+sqrt(1+x^2))^n` then `(1+x^2)(d^2y)/(dx^2)+x(dy)/(dx)`

A

`n ^(2)y`

B

`y ^(-n^(2))`

C

`-y`

D

`2x ^(2)y`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION

    VK JAISWAL|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|36 Videos
  • CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION

    VK JAISWAL|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|32 Videos
  • COMPOUND ANGLES

    VK JAISWAL|Exercise Exercise-5 : Subjective Type Problems|31 Videos
  • DETERMINANTS

    VK JAISWAL|Exercise EXERCISE-4 : SUBJECTIVE TYPE PROBLEMS|11 Videos

Similar Questions

Explore conceptually related problems

If y=(x+sqrt(1+x^(2)))^(n) then (1+x^(2))(d^(2)y)/(dx^(2))+x(dy)/(dx)

If y= sin (mlog (x+ sqrt( 1+x^(2)))),then (1+x^(2) ) (d^(2)y)/(dx^(2))+x(dy)/(dx) =

If y=[x+sqrt(x^(2)-1)]^(15)+[x-sqrt(x^(2)-1)]^(15) then (x^(2)-1)(d^(2)y)/(dx^(2))+x(dy)/(dx) is eqaul to

If y=(x+sqrt(1+x^(2)))^(n), then show that (1+x^(2))(d^(2)y)/(dx^(2))+x(dy)/(dx)=n^(2)y

If y=(sin^(-1)x)^2 then prove that (1-x^(2))(d^2y)/(dx^2)-x(dy)/(dx)-2=0 .

VK JAISWAL-CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION-EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. If y=(x+sqrt(1+x^2))^n then (1+x^2)(d^2y)/(dx^2)+x(dy)/(dx)

    Text Solution

    |

  2. Let f (x)= {{:(ac (x-1)+b,,, x lt 1),( x+2,,, 1 le x le 3),(px ^(2) +q...

    Text Solution

    |

  3. If y= sin (8 sin ^(-1) x ) then (1-x ^(2)) (d^(2)y)/(dx ^(2))-x (dy)/...

    Text Solution

    |

  4. If y ^(2) =4ax, then (d^(2) y)/(dx ^(2))=(ka ^(2))/( y ^(2)), where k ...

    Text Solution

    |

  5. The number of values of x , x I [-2,3] where f (x) =[x ^(2)] sin (pix)...

    Text Solution

    |

  6. If f (x) is continous and fifferentiable in [-3,9] and f'(x) in [-2,8]...

    Text Solution

    |

  7. In f (x)= [{:(cos x ^(2),, x lt 0), ( sin x ^(3) -|x ^(3)-1|,, x ge 0)...

    Text Solution

    |

  8. Let f (x) =x ^(2) +ax+3 and g (x) =x+b, where F (x) =lim (xto oo) (f(x...

    Text Solution

    |

  9. Let f (x)= {{:(2-x"," , -3 le x le 0),( x-2"," , 0 lt x lt 4):} Then f...

    Text Solution

    |

  10. If f (x) +2 f (1-x)( =x ^(2) +2AA x in R and f (x) is a differentiable...

    Text Solution

    |

  11. Let f (x)= signum (x) and g (x) =x (x ^(2) -10x+21), then the number o...

    Text Solution

    |

  12. If (d^(2))/(d x ^(2))((sin ^(4)x+ sin ^(2)x+1)/(sin ^(2)x + si n x+1))...

    Text Solution

    |

  13. f (x) =a cos (piy)+b, f'((1)/(2))=pi and int (1//2)^(3//2) f (x) dx =2...

    Text Solution

    |

  14. Let alpha (x) = f(x) -f (2x) and beta (x) =f (x) -f (4x) and alpha '(1...

    Text Solution

    |

  15. Let f (x) =-4.e ^((1-x)/(2))+ (x ^(3))/(3 ) + (x ^(2))/(2)+ x+1 and g ...

    Text Solution

    |

  16. If y=3^(2 sin ^(-1)) then |((x ^(2) -1) y ^(+) +xy')/(y)| is equal to

    Text Solution

    |

  17. Let f (x)=x+ (x ^(2))/(2 )+ (x ^(3))/(3 )+ (x ^(4))/(4 ) +(x ^(5))/(5)...

    Text Solution

    |

  18. In f (x)= [{:(cos x ^(2),, x lt 0), ( sin x ^(3) -|x ^(3)-1|,, x ge 0)...

    Text Solution

    |

  19. Let f :R to R be a differentiable function satisfying: f (xy) =(f(x)...

    Text Solution

    |

  20. For the curve sin x + si y=1 lying in the first quadrant there exist a...

    Text Solution

    |

  21. Let f (x) = x tan ^(-1) (x^(2)) + x^(4) Let f ^(k) (x) denotes k ^(th)...

    Text Solution

    |