Home
Class 12
MATHS
Find . (d^2y)/(dx^2),ifx=a t^2,y=2a tdot...

Find . `(d^2y)/(dx^2),ifx=a t^2,y=2a tdot`

Text Solution

Verified by Experts

Given, `x=a t^2,y=2a t`
On differentiating both sides w.r.t. t, we get,
`(dx)/(dt)​=2at` and `(dy)/(dt)​=2a`
Therefore,
`(dy)/(dx)=1/t`
...
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

Find (dy)/(dx) , if x=a t^2, y=2a t .

Find (dy)/(dx) , if x=a t^2 , y=2a t

Find (dy)/(dx) , if x=2a t^2 , y=a t^4

(The value of (d^(2)y)/(dx^(2)) is) (i) if x=t^2,y=t^3.

IF x=2at^2,y=at^4 , then (d^2y)/(dx^2) at t=2 is

Find (d^(2)y)/(dx^(2)) when y=logx/x .

If x=2at^3,y=at^4 , then (d^2y)/(dx^2) at t=2 is

RD SHARMA-HIGHER ORDER DERIVATIVES-Solved Examples And Exercises
  1. If y=(logx)/x ,s howt h a t(d^2y)/(dx^2)=(2logx-3)/(x^3)

    Text Solution

    |

  2. If y=2 sin x+3cos x, show that (d^2y)/(dx^2)+y=0

    Text Solution

    |

  3. Find . (d^2y)/(dx^2),ifx=a t^2,y=2a tdot

    Text Solution

    |

  4. If x=sin theta,y=cosptheta,p rov et h a t (1-x^2)y2-x y1+p^2y=0,w ...

    Text Solution

    |

  5. If y=tan^-1x find (d^2y)/(dx^2) in terms of y alone.

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |