Home
Class 12
MATHS
The differential coefficient of f(loge x...

The differential coefficient of `f(log_e x) w.r.t. x,` where `f(x) = log_e x,` is (i) `x/lnx` (ii) `lnx/x` (iii) `1/(xlnx)` (iv) `xlnx`

A

`(x)/(log_(e)x)`

B

`(1)/(x)log_(e)x`

C

`(1)/(xlog_(e)x)`

D

none of these

Text Solution

Verified by Experts

`f(log_(e)x)=log_(e)(log_(e)x)`
`therefore" "(df(log_(e)x))/(dx)=(1)/(log_(e)x)xx(1)/(x)`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise (Multiple)|22 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise (Comprehension)|23 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise 3.9|14 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|25 Videos

  • DOT PRODUCT

    CENGAGE|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

The differential coefficient of f(log_(e)x)w*r.t.x, where f(x)=log_(e)x, is (i) (x)/(ln x)( ii) (ln x)/(x)( iii) (1)/(x ln x)( iv )x ln x

Differential coefficient of log_2(log_2x )w.r.t x is______

The differential coefficient of f((log)_e x) with respect to x , where f(x)=(log)_e x , is (a)x/((log)_e x) (b) 1/x(log)_e x (c)1/(x(log)_e x) (d) none of these

The derivative of function f(x) = log_e(2x) w.r.t. t is

The differential coefficient of f(log x) with respect to x, where f(x)=log x is (x)/(log x) (b) (log x)/(x)(c)(x log x)^(-1)(d) none of these

CENGAGE-DIFFERENTIATION-Exercise (Single)
  1. if y=log(sinx) tanx then ((dy)/(dx)) (pi/4) is

    Text Solution

    |

  2. d/(dx)[sin^2cot^(- 1)sqrt((1-x)/(1+x))] is

    Text Solution

    |

  3. The differential coefficient of f(loge x) w.r.t. x, where f(x) = loge...

    Text Solution

    |

  4. if f'(x)=sqrt(2x^2-1) and y=f(x^2) then (dy)/(dx) at x=1 is:

    Text Solution

    |

  5. If u=f(x^3),v=g(x^2),f^(prime)(x)=cosx ,a n dg^(prime)(x)=sinx ,t h e ...

    Text Solution

    |

  6. A function f, defined for all positive real numbers, satisfies the equ...

    Text Solution

    |

  7. Let f : (-5,5)rarrR be a differentiable function of with f(4) = 1, f'(...

    Text Solution

    |

  8. The function f(x)=e^(x)+x, being differentiable and one- to -one, has ...

    Text Solution

    |

  9. If f(x) = x + tan x and f is the inverse of g, then g'(x) is equal to

    Text Solution

    |

  10. If f(x)=x^(3)+3x+4 and g is the inverse function of f(x), then the val...

    Text Solution

    |

  11. If y=(sin^(-1)x)/(sqrt(1-x^2)),t h e n((1-x^2)dy)/(dx) is equal to x+y...

    Text Solution

    |

  12. " If "y=sqrt(logx+sqrt(logx+sqrt(logx+...oo)))," then "(dy)/(dx) is

    Text Solution

    |

  13. d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))]=

    Text Solution

    |

  14. Suppose the function f(x)-f(2x) has the derivative 5 at x=1 and deriva...

    Text Solution

    |

  15. If ysqrt(x^2+1)=log(sqrt(x^2+)1-x),s howt h a t(x^2+1)(dy)/(dx)+x y+1=...

    Text Solution

    |

  16. "Let "e^(y)=(sqrt(1+alpha)+sqrt(1-alpha))/(sqrt(1+alpha)-sqrt(1-alpha)...

    Text Solution

    |

  17. The derivative of tan^(-1)((sqrt(1+x^2)-1)/x) with respect to tan^(-1)...

    Text Solution

    |

  18. If ln((e-1)e^(xy) +x^2)=x^2+y^2 then ((dy)/(dx))(1,0) is equal to

    Text Solution

    |

  19. If y=(x^x)^x then (dy)/(dx) is

    Text Solution

    |

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

    Text Solution

    |