Home
Class 12
MATHS
If x=f(t) and yy=g(t) are differentia...

If `x=f(t)` and yy=g(t) are differentiable functions of t then `(d^(2)y)/(dx^(2))` is

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

`(g'(t).f''(t)-f'(t).f''(t))/[f'(t)]^3`

D

`(g'(t).f''(t)+f'(t).f''(t))/[f'(t)]^3`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    TARGET PUBLICATION|Exercise EVALUATION TEST|30 Videos

  • DIFFERENTIATION

    TARGET PUBLICATION|Exercise HIGHER ORDER DERIVATIVES|32 Videos

  • DIFFERENTIAL EQUATIONS

    TARGET PUBLICATION|Exercise EVALUATION TEST|25 Videos

  • INTEGRATION

    TARGET PUBLICATION|Exercise EVALUATION TEST|29 Videos

Similar Questions

Explore conceptually related problems

If x = f(t) and y = g(t) are differentiable functions of t so that y is a differentiable functions of x and if dx//dt ne 0 then (dy)/(dx) =(dy)/((dt)/((dx)/(dt)) . Hence find dy/dx if x= 2sint and y=cos2t

Differentiate the function w.r.t x : e^(x^2)

If x=f(t), y=g(t) are differentiable functions of parameter 't' then prove that y is a differentiable function of 'x' and (dy)/(dx)=((dy)/(dt))/((dx)/(dt)),(dx)/(dt) ne 0 Hence find (dy)/(dx) if x=a cos t, y= a sin t.

Differentiate the function f(t)=sqrt(t)(1-t)

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

Differentiate the function w.r.t x : x^2cos x

Differentiate the functions given in w.r.t. x : (x+7)^(2)*(x+4)^(3) .

Differentiation of x^2 w.r.t. x is

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

TARGET PUBLICATION-DIFFERENTIATION -COMPETITIVE THINKING
  1. If u = x^(2) + y^(2) " and " x = s + 3t, y = 2s - t , " then " (d^(2...

    Text Solution

    |

  2. If x=at^2,y=2at, then (d^2x)/(dy^2)=

    Text Solution

    |

  3. If x=f(t) and yy=g(t) are differentiable functions of t then (d^...

    Text Solution

    |

  4. If y=(x+sqrt(1+x^2))^n then (1+x^2)(d^2y)/(dx^2)+x(dy)/(dx)

    Text Solution

    |

  5. If x^2y^3=(x+y)^5, then (d^2y)/(dx^2) is

    Text Solution

    |

  6. If x=sint and y=sinp t , prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)+p^...

    Text Solution

    |

  7. If x=costheta, y=sin5theta then (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)=

    Text Solution

    |

  8. If y=e^sqrtx+e^(-sqrtx), then (x(d^2y)/(dx^2)+1/2.(dy)/(dx)) is equal ...

    Text Solution

    |

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

    Text Solution

    |

  10. If x=acostheta,y=bsintheta , then (d^2y)/(dx^2) when theta=pi/4 is gi...

    Text Solution

    |

  11. If y = x^(3)log ( log (1+x) ) ,theny''(0) =

    Text Solution

    |

  12. If x=e^t sin t , y=e^t cos t, t is a parameter , then (d^2y)/(dx^2) at...

    Text Solution

    |

  13. If x=3 cos t and y=4 sin t, then (d^2y)/(dx^2) at the point (x0,y0)=(3...

    Text Solution

    |

  14. If f:R in R is defined by f(x)=(x^(2)-ax+1)/(x^(2)+ax+1),0ltalt2, th...

    Text Solution

    |

  15. If y=(a^(cos^-1x))/(1+a^(cos^-1x))andz=a^(cos^-1x),then (dy)/(dx)=

    Text Solution

    |

  16. The first derivative of the function [cos^(-1)(sin sqrt((1+x)/2))+x^x]...

    Text Solution

    |

  17. Let g(x) be the inverse of the function f(x), and f'(x)=1/(1+x^3) then...

    Text Solution

    |

  18. Let f(x)=tan^-1 x. Then, f'(x)+f''(x) is = 0, when x is equal to

    Text Solution

    |

  19. If x=a(t-(1)/(t)),y=a(t+(1)/(t)),"show that "(dy)/(dx)=(x)/(y)

    Text Solution

    |

  20. If 2y=sin^-1(x+5y),then,(dy)/(dx) is equal to

    Text Solution

    |