Home
Class 12
MATHS
Let g(x) be the inverse of the function ...

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

A

`1/(1+[g(x)]^3)`

B

`1/(1+[f(x)]^3)`

C

`1+[g(x)]^3`

D

`1+[f(x)]^3`

Text Solution

Verified by Experts

The correct Answer is:
C
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 g is the inverse of a function f and f'(x) = 1/(1+x^(5)) , then g'(x) is equal to

If g(x) is the inverse function of f(x) and f'(x)=(1)/(1+x^(4)) , then g'(x) is

If g is the inverse of a function f and f'(x)=(1)/(1+x^(n)), g'(x) is equal to

Let g(x) be the inverse of f(x) and f'(x)=1/(1+x^(3)) .Find g'(x) in terms of g(x).

If g is the inverse of f and f'(x) = (1)/(1 + x^(2)) , then g'(x) is equal to

TARGET PUBLICATION-DIFFERENTIATION -COMPETITIVE THINKING
  1. If x^2y^3=(x+y)^5, then (d^2y)/(dx^2) is

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. Let f:R to R be a function such that f(x+y)=f(x)+f(y)"for all", x,y in...

    Text Solution

    |

  18. If x^2+y^2=(t+1/t) and x^4+y^4=t^2+1/t^2, then x^3y(dy)/(dx)=

    Text Solution

    |

  19. Let f1(x)=e^x,f2(x)=e^(f1(x)),"........",f(n+1)(x)=e^(fn(x)) for all n...

    Text Solution

    |

  20. Let f: R to R be a dIfferentiable function . If f is even, then f'(0) ...

    Text Solution

    |