Home
Class 12
MATHS
If y^3-y=2x ,p rov et h a t(d^2y)/(dx^2...

If `y^3-y=2x ,p rov et h a t(d^2y)/(dx^2)=(-24 y)/((3y^2-1)^3)`

Text Solution

Verified by Experts

`y^3−y=2x`
differentiate on both sides w.r.t `x`
`3y^2(dy)/(dx)​−(dy)/(dx)​=2 (dy)/(dx)​=2/((3y^2−1))​`
Again differentiate on both sides w.r.t x
`=> (d^2y)/(dx^2)​
=(-2)/((3y2−1)^2)​(6y)(dy​)/(dx)` ...
Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|393 Videos

  • INCREASING AND DECREASING FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|232 Videos

Similar Questions

Explore conceptually related problems

If y^(3)-y=2x, prove that (d^(2)y)/(dx^(2))=-(24y)/((3y^(2)-1)^(3))

If sqrt(1-x^6)+sqrt(1-y^6)=a(x^3-y^3),p rov et h a t(dy)/(dx)=(x^2)/(y^2)sqrt((1-y^6)/(1-x^6,) w h e r e-1x,1a n d-1

x=a sec theta,y=b tan theta,pr@v et h a t(d^(2)y)/(dx^(2))=-(b^(4))/(a^(2)y^(3))

If y = sin3x then (d^2y)/(dx^2) =?

If x^(3)+y^(3)-3axy=0 then prove that (d^(2)y)/(dx^(2))=(2a^(2)xy)/((ax-y^(2))^(3))

If x=a(1-cos^3theta),y=asin^3theta,"p r o v et h a t"(d^2y)/(dx^2)=(32)/(27a) "at" theta=pi/6dot

If x^(3)+y^(3)=t-(1)/(t) and x^(6)+y^(6)=t^(2)+(1)/(t^(2)) then prove that (d^(2)y)/(dx^(2))=(2y)/(x^(2))

If y=sin^(-1)x, show that (d^(2)y)/(dx^(2))=(1)/((1-x^(2))^(3/2))

If y=sqrt(sinx+sqrt(sinx+sqrt(sinx+ tooo))),p rov et h a t(dy)/(dx)=(cosx)/(2y-1)

y sqrt(1-x^(2))+x sqrt(1-y^(2))=1,prov et h a t (dy)/(dx)=sqrt((1-y^(2))/(1-x^(2)))

RD SHARMA-HIGHER ORDER DERIVATIVES-Solved Examples And Exercises
  1. If y=tan^-1x find (d^2y)/(dx^2) in terms of y alone.

    Text Solution

    |

  2. If x^m y^n=(x+y)^(m+n), prove that (d^2y)/(dx^2)=0

    Text Solution

    |

  3. If y^3-y=2x ,p rov et h a t(d^2y)/(dx^2)=(-24 y)/((3y^2-1)^3)

    Text Solution

    |

  4. If y=x^x ,fin d(d^2y)/(dx^2)

    Text Solution

    |

  5. If y=sin^(-1)x ,s howt h a t(d^2y)/(dx^2)=x/((1-x^2)^(3/2))

    Text Solution

    |

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

    Text Solution

    |

  7. If y=tanx+secx ,p rov et h a t(d^2y)/(dx^2)=(cosx)/((1-sinx)^2)

    Text Solution

    |

  8. If y=(a x+b)/(x^2+c), then (2x y1+y) y3=

    Text Solution

    |

  9. If y=(log)e(x/a)^x ,then x^3y2=

    Text Solution

    |

  10. If sin^(-1) (1 – x) – 2sin^(-1) x = π / 2,then x is equal to

    Text Solution

    |

  11. If y=2/(sqrt(a^2-b^2)){tan^(-1)((a-b)/(a+b))tanx/2} , then show that (...

    Text Solution

    |

  12. If y=x^(n-1)lnx then x^2y2+(3-2n)x y1 is equal to -(n-1)^2y (b) (n...

    Text Solution

    |

  13. If x y-(log)e y=1 satisfies the equation x(y y2+y1 2)-y2+lambday y1=0,...

    Text Solution

    |

  14. If x=f(t )cost-f^(prime)(t)sinta n dy=f(t)sint+f^(prime)(t)cost ,t h ...

    Text Solution

    |

  15. If x=f(t) and y=g(t), then (d^2y)/(dx^2) is equal to

    Text Solution

    |

  16. Let f(x) be a polynomial.Then, the second order derivative of f(e^x) ...

    Text Solution

    |

  17. If y=tan^-1((log(e/x^2))/(log(ex^2)))+tan^-1((3+2logx)/(1-6logx)), the...

    Text Solution

    |

  18. If f(x)=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)fx-xy(x)= 1 (b) -1...

    Text Solution

    |

  19. If f(x)=(cosx+isinx)(cos2x+isin2x)(cos3x+isin3x)......(cosn x+isinn x)...

    Text Solution

    |

  20. (d^(20))/(dx^(20))(2cosxcos3x)is equal to (a)2^(20)(cos2x-2^(20)cos3x...

    Text Solution

    |