Home
Class 12
MATHS
A function f(x) is so defined that for a...

A function `f(x)` is so defined that for all real `x,{f(x)}^n = f(nx).` Prove that `f(x) · f '(nx) = f'(x) · f(nx).`

Promotional Banner

Topper's Solved these Questions

  • Differentiation

    A DAS GUPTA|Exercise Exercise|98 Videos

  • Differential Equation of the First Order

    A DAS GUPTA|Exercise Exercise|64 Videos

  • Elementary Probability

    A DAS GUPTA|Exercise Exercise|137 Videos

Similar Questions

Explore conceptually related problems

A function f is defined such that for all real x,y(a)f(x+y)=f(x).f(y)(b)f(x)=1+xg(x) where lim_(x rarr0)g(x)=1 prove that f;(x)=f(x) and f(x)=e^(x)

The function f(x) is defined for all real x .If f(x+y)=f((xy)/(4))AA x y and f(-4)=-4 then |f(2016)| is

A function f(x) is defined for all real x and satisfied f(x+y)=f(xy),AA x,y. If f(1)=-1 then f(2006) equals

The function fis not defined for =0, but for all non zero real number x,f(x)+2f((1)/(x))=3x. The equation f(x)=f(-x) is satisfied by

Given a differentiable function f(x) defined for all real x, and is such that f(x+h)-f(x)<=6h^(2) for all real h and x . Show that f(x) is constant.

If f: R to [0,∞) be a function such that f(x -1) + f(x + 1) = sqrt3(f(x)) then prove that f(x + 12) = f(x) .

A function f: R to R is defined as f(x)=4x-1, x in R, then prove that f is one - one.

Let f be a twice differentiable function defined on R such that f(0) = 1, f'(0) = 2 and f '(x) ne 0 for all x in R . If |[f(x)" "f'(x)], [f'(x)" "f''(x)]|= 0 , for all x in R , then the value of f(1) lies in the interval:

Let f(x+y)=f(x)+f(y) for all real x,y and f'(0) exists.Prove that f'(x)=f'(0) for all x in R and 2f(x)=xf(2)

Let (x) is a real function, defines as f(x) =(x-1)/(x+1), then prove that f(2x)=(3f(x)+1)/(f(x)+3).

A DAS GUPTA-Differentiation-Exercise
  1. Let f(x+y)=f(x)+f(y) for all real x,y and f'(0) exists. Prove that f'(...

    Text Solution

    |

  2. Let f((x+y)/(2))=1/2 |f(x) +f(y)|for all real x and y, if f '(0) exist...

    Text Solution

    |

  3. A function f(x) is so defined that for all real x,{f(x)}^n = f(nx). Pr...

    Text Solution

    |

  4. Prove that the derivative of (a) an odd function is an even function;

    Text Solution

    |

  5. Prove that the derivative of a periodic function of period T is a peri...

    Text Solution

    |

  6. Let f(x) be a function satisfying the condition f(-x) = f(x) for all r...

    Text Solution

    |

  7. A function f:R->R satisfies the relation f((x+y)/3)=1/3|f(x)+f(y)+f(0)...

    Text Solution

    |

  8. Find the sum of series sum(r=1)^nr.x^(r-1), using calculus.

    Text Solution

    |

  9. Differential coefficient of log2(log2x)w.r.t x is

    Text Solution

    |

  10. If f(x)=logx(logex) then f'(e)=

    Text Solution

    |

  11. If x=a (cos t +log (tan ((t)/(2)) )) ,y =a sin t ,then (dy)/(dx) =

    Text Solution

    |

  12. Let f'(x) = sin(x^2) and y = f(x^2 +1) then dy/dx at x=1 is

    Text Solution

    |

  13. If x=cost , y=loget then at t=pi/2, (d^2y)/(dx^2)+((dy)/(dx))^2=

    Text Solution

    |

  14. If f'(x)=sin x^2 and y=f(x^2+1) then dy/dx=

    Text Solution

    |

  15. If x=cost , y=loget then at t=pi/2, (d^2y)/(dx^2)+((dy)/(dx))^2=

    Text Solution

    |

  16. If tany = (2t)/(1-t^2) and sin x = (2t)/(1+t^2) then (dy)/(dx)=

    Text Solution

    |

  17. If xe^(xy)=y+sin^2x then at x=0 (dy)/dx=

    Text Solution

    |

  18. If x^2y +y^3=2, the value of (dy)/(dx) at the point (1,1) is

    Text Solution

    |

  19. Let f(x)={(tan)pi/4+tanx}{(tan)pi/4+(tan)(pi/4-x)}and g(x)=x^2+1. Then...

    Text Solution

    |

  20. IF y = 1 / (1+ x + x^2 + x^3), then value of (d^2y) / dx^2 at x = 0 is

    Text Solution

    |