Home
Class 12
MATHS
If x=f(t) and y=g(t) , then write the va...

If `x=f(t)` and `y=g(t)` , then write the value of `(d^2y)/(dx^2)` .

A

`(f'(t) g''(t) - g'(t) f''(t))/({f'(t)}^(3))`

B

`(f'(t) g''(t) - g'(t) f''(t))/({f'(t)}^(2))`

C

`(f'(t) g''(t) - g''(t) f''(t))/({f'(t)}^(2))`

D

`(f'(t) g''(t) - g''(t) f''(t))/({f'(t)}^(3))`

Text Solution

Verified by Experts

The correct Answer is:
A
Given , ` x = f(t) , y = g (t)`
`rArr (dx)/(dt) = f'(t), (dy)/(dt) = g' (t)`
` therefore (dy)/(dx) = (g'(t))/(f'(t))`
Now , `(d^(2)y)/(dx^(2)) = (d)/(dx) ((dy)/(dx)) = (d)/(dt) ((g'(t))/(f'(t))) (dt)/(dx)`
` = [ (f'(t) .g''(t) - g'(t) f''(t))/((f'(t))^(2))].(1)/(f'(t))`
`(f'(t) .g''(t) - g'(t) f''(t))/({f'(t)^(3)})`.
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 2 (MISCELLANEOUS PROBLEMS)|80 Videos

  • DIFFERENTIAL EQUATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|27 Videos

  • FACTORIZATION FORMULAE

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 2|21 Videos

Similar Questions

Explore conceptually related problems

If x=f(t) and y=g(t), then write the value of (d^(2)y)/(dx^(2))

If x=a(cos t+t sin t) and y=a(sin t-t cos t), then find the value of (d^(2)y)/(dx^(2)) at t=(pi)/(4)

If x=a(cos t+t sin t) and y=a(sin t-t cos t), then find the value of (d^(2)y)/(dx^(2)) at t=(pi)/(4)

If x=a(sin t-t cos t),y=a sin t then find the value of (d^(2)y)/(dx^(2))

If x = 3 tant and y = 3 sec t, then the value of (d^2y)/(dx^2)" at" t=pi/4 is

If x=a(cos t+t sin t) and y=a(sin t-t cos t),then find the value of (d^(2)y)/(dx^(2)) at t=(pi)/(4)

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIATION -MHT CET CORER
  1. Differentiate (logx)^x with respect to logx .

    Text Solution

    |

  2. If x sec theta , y = tan theta , then the value of (d^(2) y)/(dx^(...

    Text Solution

    |

  3. If x=f(t) and y=g(t) , then write the value of (d^2y)/(dx^2) .

    Text Solution

    |

  4. Find (dy)/(dx) , " if x " = 2 cos theta - cos 2 theta and y = 2sin...

    Text Solution

    |

  5. find the derivative of e^(x) + e^(y) = e^(x +y)

    Text Solution

    |

  6. If xy = tan^(-1) (xy) + cot^(-1) (xy), " then" (dy)/(dx) is equal to

    Text Solution

    |

  7. The derivative of cos^(3)x w.r.t. sin^(3)x is

    Text Solution

    |

  8. The derivative of log|x| is

    Text Solution

    |

  9. The function f(x)=e^(-|x|) is

    Text Solution

    |

  10. If f(x)=sin^(-1) ((2x)/(1+x^2)) then f(x) is differentiable on

    Text Solution

    |

  11. If y = log(cos x) sin x " then" (dy)/(dx) is equal to

    Text Solution

    |

  12. If y^(2) = ax^(2) + bx + c , where a,b,c, are constants , then y^...

    Text Solution

    |

  13. If x=phi(t),y=Psi(t)," then "(d^(2)y)/(dx^(2)) is equal to

    Text Solution

    |

  14. If y = 5^(x) x^(5) , " then" (dy)/(dx) is

    Text Solution

    |

  15. If y = tan^(-1) ((a cos x - b sin x)/(b cos x + a sin x)) " then " (dy...

    Text Solution

    |

  16. (d)/(dx)[sec{cos^(-1) ((x)/(8))}] is equal to

    Text Solution

    |

  17. If f(x)=sqrt(1+cos^2(x^2)),t h e nf^(prime)((sqrt(pi))/2) is

    Text Solution

    |

  18. If y = a sin^(3) theta " and " x = a cos^(3) theta . " then at " th...

    Text Solution

    |

  19. If y=sqrt(sinx+sqrt(sinx+sqrt(sinx+ . . .oo))), then (dy)/(dx) is equa...

    Text Solution

    |

  20. The nth derivatiive of (x+1)^n is

    Text Solution

    |