Home
Class 12
MATHS
If g is the inverse function of f and f'...

If g is the inverse function of f and `f'(x)= frac{1}{1+x^7}`, then the value of g'(x)........ A) 1+`x^7` B) `frac{1}{1+[g(x)]^7}` C) `1+[g(x)]^7` D) `7x^6`

A

1+`x^7`

B

`frac{1}{1+[g(x)]^7}`

C

1+`[g'(x)]^7`

D

7`x^6`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • Differentiation

    CHETANA PUBLICATION|Exercise Exercise|127 Videos
  • DIFFERENTIAL EQUATIONS

    CHETANA PUBLICATION|Exercise EXERCISE|254 Videos
  • Indefinite Integration

    CHETANA PUBLICATION|Exercise Exercise|221 Videos

Similar Questions

Explore conceptually related problems

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^(5)) , then g'(x) is equal to

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

If the function f(x)=x^(3)+e^(x//2)andg(x)=f^(-1)(x) , then the value of g'(1) is

If 1/(6!) + 1/(7!) = x/(8!) , then the value of x is

If f(x) = frac {x^2 -1}{x^2 +1} , for every real x, then the minimum value of f(x) is.

Verify Rolle's theorem for the function: f(x) = frac {2}{e^x + e^(-x) on [-1,1]

If y= cot^(-1)(frac {1-3x^2}{3x - x^3}) , then dy/dx =....... A) frac{3}{1+x^2} B) frac{2}{1-x^2} C) frac{1}{1+x^2} D) frac{1}{3(1+x^2)}

CHETANA PUBLICATION-Differentiation-Exercise
  1. If y= tan^(-1) (frac{x}{1+ sqrt (1 - x^2)}) + sin[ 2tan^(-1) (sqrt ((1...

    Text Solution

    |

  2. If y is a function of x and log(x+y) = 2xy, then the value of y'(0) = ...

    Text Solution

    |

  3. If g is the inverse function of f and f'(x)= frac{1}{1+x^7}, then the ...

    Text Solution

    |

  4. If x sqrt (y+1) + y sqrt (x+1) =0 and x != y then dy/dx=............ A...

    Text Solution

    |

  5. If y= tan^(-1) (sqrt (frac {a-x}{a+x})), where -a < x < a then dy/dx= ...

    Text Solution

    |

  6. If x= a(costheta + sintheta), y= a(sintheta + costheta), then (d^2y)/(...

    Text Solution

    |

  7. If y= a cos(log x) and A ((d^2 y)/(dx^2)) + B (dy/dx) + C = 0 , then ...

    Text Solution

    |

  8. If x^y = e^(x-y), then dy/dx = ............ A) frac{1 + x}{1+ log x} ...

    Text Solution

    |

  9. If y= 1- cos theta, x= 1- sin theta, then dy/dx at theta = pi /4 is......

    Text Solution

    |

  10. If sec(frac{x+y}{x-y}) = a^2, then (d^2 y)/(dx^2) = ............ A) y...

    Text Solution

    |

  11. If y = sec^(-1) (frac{sqrt x - 1}{x+sqrt x}) + sin^(-1) (frac{x + sqr...

    Text Solution

    |

  12. Derivative of tan^3theta with respect to sec^3theta at theta = (pi/3) ...

    Text Solution

    |

  13. If x^5y = (x+y)^(n-2) and dy/dx = y/x, then n=..........

    Text Solution

    |

  14. If x= e^2log(e)(sin theta), y= e^2log(e)(cos theta), then dy/dx at ...

    Text Solution

    |

  15. If y= sqrt (log x + sqrt (log x + sqrt (log x + .......oo))), then dy/...

    Text Solution

    |

  16. If y= 5^(2log(5)(sin x)) + 7^(2log(7)(cos x)), then dy/dx= A) 1 B) -...

    Text Solution

    |

  17. If y= (sin^(-1) x)^2, then (1-x^2) (d^2 y)/(dx^2) - x (dy/dx) = .........

    Text Solution

    |

  18. If y= sin^(-1) (frac{5x+ 12 sqrt (1-x^2)}{13}), then (dy/dx) = ..........

    Text Solution

    |

  19. If x= a(theta - sin theta), y= a(1- cos theta), then dy/dx=......... A...

    Text Solution

    |

  20. If x= a cos^3 t, y= a sin^3 t, then dy/dx=..... A) -y/x B) -(y/x)^(1...

    Text Solution

    |