Home
Class 12
MATHS
Let x=f(t) and y=g(t), where x and y are...

Let x=f(t) and y=g(t), where x and y are twice differentiable function. If f'(0)= g'(0) =f''(0) = 2. g''(0) = 6, then the value of `((d^(2)y)/(dx^(2)))_(t=0)` is equal to

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

`"We have "(dy)/(dx)=(g'(t))/(f'(t))`
`rArr" "(d)/(dx)((dy)/(dx))=(d)/(dx)((g'(t))/(f'(t)))`
`=(d)/(dt)((g'(t))/(f'(t))).(dt)/(dx)`
`=(f'(t)g''(t)-g'(t)f''(t))/((f'(t))^(2))cdot(dt)/(dx)`
`rArr" "((d^(2)y)/(dx^(2)))_(t=0)=(f'(0)g''(0)-g'(0)f''(0))/((f'(0))^(3))`
`=(2xx6-2xx2)/(2^(3))`
`=1`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise (Multiple)|22 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise (Comprehension)|23 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise 3.9|14 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|25 Videos

  • DOT PRODUCT

    CENGAGE|Exercise DPP 2.1|15 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=f(t) and yy=g(t) are differentiable functions of t then (d^(2)y)/(dx^(2)) is

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

fis a differentiable function such that x=f(t^(2)),y=f(t^(3)) and f'(1)!=0 if ((d^(2)y)/(dx^(2)))_(t=1)=

Let f(x)and g(x) be twice differentiable functions on [0,2] satisfying f''(x)=g''(x) , f'(1)=4 , g'(1)=6 , f(2)=3 and g(2)=9 . Then what is f(x)-g(x) at x=4 equal to ?

Let f : (-1,1) to R be a differentiable function with f(0) =-1 and f'(0)=1 Let g(x)= [f(f(2x)+1)]^2 . Then g'(0)=

CENGAGE-DIFFERENTIATION-Exercise (Single)
  1. f(x)=e^(x)-e^(-x)-2 sin x -(2)/(3)x^(3). Then the least value of n for...

    Text Solution

    |

  2. Let y=f(x) and x=(1)/(z)." If "(d^(2)y)/(dx^(2))=lamda(z^(3))(dy)/(dz)...

    Text Solution

    |

  3. Let x=f(t) and y=g(t), where x and y are twice differentiable function...

    Text Solution

    |

  4. If f(x) satisfies the relation f((5x-3y)/2)=(5f(x)-3f(y))/2AAx ,y in ...

    Text Solution

    |

  5. A function f: RvecR satisfies xcosy(f(2x+2y)-f(2x-2y)=cosxsiny(f(2x+2y...

    Text Solution

    |

  6. If y=asinx+bcosx , then y^2+((dy)/(dx))^2 is a

    Text Solution

    |

  7. d/(dx)sqrt((1-sin2x)/(1+sin2x))i se q u a lto,(0<x<pi/2), sec^2x (b) ...

    Text Solution

    |

  8. If f(x) = |cos x| + |sin x|, then dy/dx at x = (2pi)/3 is equal to

    Text Solution

    |

  9. If f(x) =|log(e)|x||, then f'(x) equals

    Text Solution

    |

  10. If f(x)=sqrt(1-sin2x) , then f^(prime)(x) is equal to -(cosx+sinx),for...

    Text Solution

    |

  11. Instead of the usual defination of derivatie Df(x), if we define a new...

    Text Solution

    |

  12. if y=((a-x)sqrt(a-x)-(b-x)sqrt(x-b))/(sqrt(a-x)+sqrt(x-b)) then dy/dx ...

    Text Solution

    |

  13. The derivative of y=(1-x)(2-x)..........(n-x) at x=1 is equal to

    Text Solution

    |

  14. " If "y=sqrt((1-x)/(1+x))," then "(1-x^(2))(dy)/(dx) is equal to

    Text Solution

    |

  15. If y=(sqrt(a+x)-sqrt(a-x))/(sqrt(a+x)+sqrt(a-x)), then (dy)/(dx) is e...

    Text Solution

    |

  16. Let u/x a n dv(x) be differentiable functions such that (u(x))/(v(x))=...

    Text Solution

    |

  17. If sin^(-1)((x^2-y^2)/(x^2+y^2))=loga ,t h e n(dy)/(dx) is equal to x/...

    Text Solution

    |

  18. Let h(x) be differentiable for all x and let f(x)=(k x+e^x)h(x) , wher...

    Text Solution

    |

  19. If lim(trarrx) (e^(t)f(x)-e^(x)f(t))/((t-x)(f(x))^(2))=2 andf(0)=(1)/(...

    Text Solution

    |

  20. If f(0)=0,f^(prime)(0)=2, then the derivative of y=f(f(f(x))) at x=0 i...

    Text Solution

    |