Home
Class 12
MATHS
If y=(t a n^(-1)\ x^2) , show that (x^2+...

If `y=(t a n^(-1)\ x^2)` , show that `(x^2+1)^2(d^2\ y)/(dx^2)+2x(x^2+1)(dy)/(dx)=2.`

Promotional Banner

Topper's Solved these Questions

  • Continuity and Differentiability

    NAGEEN PRAKASHAN|Exercise Exercies 5m|19 Videos
  • Continuity and Differentiability

    NAGEEN PRAKASHAN|Exercise Exercies 5n|11 Videos
  • Continuity and Differentiability

    NAGEEN PRAKASHAN|Exercise Exercies 5k|12 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 y=(tan^(-1)x^(2)), show that (x^(2)+1)^(2)(d^(2)y)/(dx^(2))+2x(x^(2)+1)(dy)/(dx)=2

y=(cot^(-1)x)^(2), thenshowthat (x^(2)+1)^(2)(d^(2)y)/(dx^(2))+2x(x^(2)+1)(dy)/(dx)

If y=(cot^(-1)x)^(2) , then show that (x^(2)+1)^(2)(d^(2)y)/(dx^(2))+2x(x^(2)+1)(dy)/(dx)=2.

If y = (tan^(-1))^(2) , show that (1+x^(2))(d^(2)y)/(dx^(2)) + 2x(1+x^(2))(dy)/(dx) - 2 = 0

If y=(tan^(-1)x)^(2), then (x^(2)+1)^(2)(d^(2)y)/(dx^(2))+2x(x^(2)+1)(dy)/(dx)=

IF y= ( tan ^(-1) x)^(2) " then " (x^(2) +1)^(2) (d^(2)y)/(dx^(2))+2x(x^(2)+1)(dy)/(dx)=

If y=(sin^(-1)x)^(2),"show that "(1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)=2

If y=tan^(-1)x, show that (1+x^(2))(d^(2)y)/(dx^(2))+2x(dy)/(dx)=0

If y=e^(2tan^(-1)x) , the show that : (1+x^(2))^(2)(d^(2)y)/(dx^(2))+2x(1+x^(2))dy/dx=4y .

If y=csc^(-1)x,x>1, then show that x(x^(2)-1)(d^(2)y)/(dx^(2))+(2x^(2)-1)(dy)/(dx)=0

NAGEEN PRAKASHAN-Continuity and Differentiability-Exercies 5l
  1. Find the 2nd derivative if x^3 log x with respect to x.

    Text Solution

    |

  2. If y=tan^(-1)x^3 then find (d^2y)/(dx^(2)).

    Text Solution

    |

  3. Find the 2nd dervative of e^(ax+b) with respect to x.

    Text Solution

    |

  4. If y=x+cotx then prove that sin^2x(d^2y)/(dx^2)-2y2x=0.

    Text Solution

    |

  5. If y=log(sinx) , prove that (d^3y)/(dx^3)=2cosx cos e c^3x .

    Text Solution

    |

  6. If y=Acosn x+Bsinn x ,s howt h a t (d^2y)/(dx^2)+n^2y=0

    Text Solution

    |

  7. (i) If y=asin(log x) then prove that x^(2)*(d^2y)/(dx^2)+x(dy)/(dx)+y=...

    Text Solution

    |

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

    Text Solution

    |

  9. If y=sin(sinx) then prove that (d^2y)/(dx^2)+tanx. (dy)/(dx)+y cos^2...

    Text Solution

    |

  10. IF y=e^(tan^(-1)x) then prove that : (1-x^(2))(d^2y)/(dx^2)+(2x-1)(d...

    Text Solution

    |

  11. If y^3-3ax^2+x^3=0, then prove that (d^2y)/(dx^2)+(2a^2x^2)/(y^5) = 0

    Text Solution

    |

  12. If y=(t a n^(-1)\ x^2) , show that (x^2+1)^2(d^2\ y)/(dx^2)+2x(x^2+1)(...

    Text Solution

    |

  13. If y=e^tanx then prove that: cos^2x(d^2y)/(dx^2)-(1+sin2x)(dy)/dx=0

    Text Solution

    |

  14. If y=A e^(-k t)cos(p t+c), then prove that (d^2y)/(dt^2)+2k(dy)/(dx)+n...

    Text Solution

    |

  15. If x=at^2,y=2 at then find (d^2y)/(dx^2).

    Text Solution

    |

  16. If x=a(t-sint), y=a(1-cost) then find (d^2y)/(dx^2).

    Text Solution

    |

  17. If x=sint" and "y=sin mt" then prove that "sqrt(1-x^2)(d^2y)/(dx^2)-xd...

    Text Solution

    |

  18. If y=(sin^(-1)x)^2+(cos^(-1)x)^2, then prove that (1-x^2)y2-xy(1)-4=0.

    Text Solution

    |