Home
Class 12
MATHS
if x=(1+t)/t^3 ,y=3/(2t^2)+2/t satisfies...

if `x=(1+t)/t^3 ,y=3/(2t^2)+2/t` satisfies `f(x)*{(dy)/(dx)}^3=1+(dy)/(dx)` then `f(x)` is:

A

`x`

B

`(x^(2))/(1+X^(2))`

C

`x+x+(1)/(x)`

D

`x-(1)/(x)`

Text Solution

Verified by Experts

The correct Answer is:
A
`(dy)/(dx)=(dy//dt)/(dx//dt)=(-((3+2r))/(t^(3)))/(-((3+2t))/(t^(4)))=t`
Since `f(x)((dy)/(dx))^(3)=1+(dy)/(dx)`
`rArr" "f(x)t^(3)=1+t`
`rArr" "f(x)=(1+t)/(t^(3))=x`
Promotional Banner

Topper's Solved these Questions

  • METHODS OF DIFFERENTIATION

    CENGAGE|Exercise Single Correct Answer Type|46 Videos

  • MATRICES

    CENGAGE|Exercise Solved Examples And Exercises|165 Videos

  • METHODS OF DIFFERETIATION

    CENGAGE|Exercise Question Bank|29 Videos

Similar Questions

Explore conceptually related problems

If x=(1+t)/(t^(3)),y=(3)/(2t^(2))+(2)/(t), then x((dy)/(dx))^(3)-(dy)/(dx) is equal to (a)0(b)-1(c)1(d)

If x=(1+t)/(t^(3)),y=(3)/(2t^(2))+(2)/(t), then x((dy)/(dx))^(3)-(dy)/(dx) is equal to a.0 b.-1 c.1 d.2

If x=(1+log t)/(t^(2)),y=(3+2log t)/(t),quad find (dy)/(dx)

If x=(1-t^2)/(1+t^2) and y=(2at)/(1+t^2) , then (dy)/(dx)=

if x=(1+ln t)/(t^(2)) and y=(3+2ln t)/(t) then show that y(dy)/(dx)=2x((dy)/(dx))^(2)+1

If x=(1+log t)/(t^(2)),y=(3+2log t)/(t), find (dy)/(dx)

If x=(3at)/(1+t^(3)),y=(3at^(2))/(1+t^(3)), then (dy)/(dx) is

If x=(1-t^2)/(1+t^2) and y=(2t)/(1+t^2) ,then (dy)/(dx)=

If x=(2t)/(1+t^(2)),y=(1-t^(2))/(1+t^(2))," then "(dy)/(dx)=

CENGAGE-METHODS OF DIFFERENTIATION-Single Correct Answer Type
  1. (d)/(dx)[cos^(-1)(xsqrtx-sqrt((1-x)(1-x^(2))))]=

    Text Solution

    |

  2. If t(1+x^2)=x and x^2+t^2=y, then at x=2 the value of (d y)/(d x) is e...

    Text Solution

    |

  3. if x=(1+t)/t^3 ,y=3/(2t^2)+2/t satisfies f(x)*{(dy)/(dx)}^3=1+(dy)/(d...

    Text Solution

    |

  4. Let y=x^3-8x+7a n dx=f(t)dot If (dy)/(dt)=2 and x=3 at t=0, then (dx)/...

    Text Solution

    |

  5. If x=sectheta-costheta and y=sec^n theta- cos^n theta then show that (...

    Text Solution

    |

  6. The derivative of the function represented parametrically as x=2t=|...

    Text Solution

    |

  7. If y = tan^(-1)(u/sqrt(1-u^2)) and x = sec^(-1)(1/(2u^2-1)), u in (0...

    Text Solution

    |

  8. The differential coefficient of sin^(-1)((5cos x-4s in x)/(sqrt(41))) ...

    Text Solution

    |

  9. x y=(x+y)6na n d(dy)/(dx)=y/x t h e nn= 1 b.2 c. 3 d. 4

    Text Solution

    |

  10. If x+y=3e^2t h e d/(dx)(x^y)=0forx= e^2 b. e^e c. e d. 2e^2

    Text Solution

    |

  11. If f(x)=(x-1)^(100)(x-2)^(2(99))(x-3)^(3(98))…(x-100)^(100), then the ...

    Text Solution

    |

  12. The function f: RvecR satisfies f(x^2)dotf^(x)=f^(prime)(x)dotf^(prime...

    Text Solution

    |

  13. The second derivative of a single valued function parametrically repre...

    Text Solution

    |

  14. For the curve sinx+siny=1 lying in first quadrant. If lim(xrarr0) x^(...

    Text Solution

    |

  15. If y=((alphax+beta)/(gammax+delta)), then 2(dy)/(dx).(d^(3)y)/(dx^(3))...

    Text Solution

    |

  16. If f(1)=3, f'(1) = 2, f''(1)=4, then (f^-)''(3)= (where f^-1=invers...

    Text Solution

    |

  17. If the third derivative of (x^(4))/((x-1)(x-2)) is (-12k)/((x-2)^(4))+...

    Text Solution

    |

  18. (a+bx)e^(y/x)=x , Prove that x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2

    Text Solution

    |

  19. If R=([1+((dy)/(dx))^2]^(-3//2))/((d^2y)/(dx2)) , thenR^(2//3) can be ...

    Text Solution

    |

  20. x= 2 cos t -cos 2t ,y=2 sin t-sin 2t

    Text Solution

    |