Home
Class 12
MATHS
Let f be a differentiable function satis...

Let f be a differentiable function satisfying
`[f(x)]^(n)=f(nx)" for all "x inR.`
Then, `f'(x)f(nx)`
a. `f(x)`
b. `0`
c. `f(x)f'(nx)`
d. none of these

A

`f(x)`

B

0

C

`f(x)f'(nx)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|8 Videos

  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|16 Videos

  • DIFFERENTIATION

    ARIHANT MATHS|Exercise SOLVED EXAMPLES|8 Videos

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|26 Videos

  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

Let f be differentiable function satisfying f((x)/(y))=f(x) - f(y)"for all" x, y gt 0 . If f'(1) = 1, then f(x) is

Let f:(0,oo)rarrR be a differentiable function such that f'(x)=2-(f(x))/(x) for all x in (0,oo) and f(1) ne 1. Then

Let f be a function satisfying f(x+y)=f(x) + f(y) for all x,y in R . If f (1)= k then f(n), n in N is equal to

If 'f' is a real valued differentiable function such that f(x) f'(x) < 0 for all real x, then

The number or linear functions f satisfying f(x+f(x))=x+f(x) AA x in RR is

Let f be a differentiable function satisfying the relation f(xy)=xf(y)+yf(x)−2xy .(where x, y >0) and f ′ (1)=3, then find f(x)

Let f be a differentiable function such that f'(x) = f(x) + int_(0)^(2) f(x) dx and f(0) = (4-e^(2))/(3) . Find f(x) .

Let f(x) be a differentiable function such that f(x)=x^2 +int_0^x e^-t f(x-t) dt then int_0^1 f(x) dx=

Let f:R to R be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt . f(x) increases for

Let the function f satisfies f(x).f ′ (−x)=f(−x).f ′ (x) for all x and f(0)=3 The value of f(x).f(-x) for all x is

ARIHANT MATHS-DIFFERENTIATION -Exercise (More Than One Correct Option Type Questions)
  1. If f(x)=sin{(pi)/(3)[x]-x^(2)}" for "2ltxlt3 and [x] denotes the grea...

    Text Solution

    |

  2. The functions u=e^(x).sinx and v=e^(x).cosx satisfy the equation

    Text Solution

    |

  3. If f(x)=log(x^(2))(logx),then f '(x)at x= e is

    Text Solution

    |

  4. Let f be a differentiable function satisfying [f(x)]^(n)=f(nx)" for ...

    Text Solution

    |

  5. If y=f(x) is an odd differentiable function defined on (-oo,oo) such t...

    Text Solution

    |

  6. "If "y=sqrt(x+sqrt(y+sqrt(x+sqrt(y+...oo))))," then prove that "(dy)/(...

    Text Solution

    |

  7. If f(x)=|cosx-sinx| , then f'(pi/4) is equal to

    Text Solution

    |

  8. Let f(x)=x^2+xg'(1)+g''(2) and g(x)=f(1).x^2+xf'(x)+f''(x), then find ...

    Text Solution

    |

  9. if f(x) = x^n then the value of f(1) - (f'(1))/(1!) + (f''(1))/(2!) +...

    Text Solution

    |

  10. If y+log(1+x)=0 which of the following is true?

    Text Solution

    |

  11. If y=2^(3^(x)), then y' equals

    Text Solution

    |

  12. If g is the inverse of fandf(x) = x^(2)+3x-3,(xgt0). then g'(1) equal...

    Text Solution

    |

  13. If x^(3)-2x^(2)y^(2)+5x+y-5=0 and y(1) = 1, then a. y'(1)=(4)/(3) b. y...

    Text Solution

    |

  14. Let y=sqrt(x+sqrt(x+sqrt(x+oo))) , (dy)/(dx) is equal to

    Text Solution

    |

  15. Ify=x^((lnx)^ln(lnx)) , then (dy)/(dx) is equal to

    Text Solution

    |

  16. Which of the following functions are not derivable at x=0?

    Text Solution

    |

  17. If 2^(x)+2^(y)=2^(x+y) then (dy)/(dx)is equal to

    Text Solution

    |

  18. For the function y=f(x)=(x^(2)+bx+c)e^(x), which of the following hold...

    Text Solution

    |

  19. If sqrt(y+x)+sqrt(y-x)=c, where cne0, then (dy)/(dx) has the value equ...

    Text Solution

    |

  20. If y = tan x tan 2x tan 3x, (sin 12x != 0) then dy / dx has the value ...

    Text Solution

    |