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y=(ln*x)/(x-1)

Derivative of y=(ln*x)/(x-1)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
log(x)
------
x - 1 
$$\frac{\log{\left(x \right)}}{x - 1}$$
log(x)/(x - 1)
Detail solution
  1. Apply the quotient rule, which is:

    and .

    To find :

    1. The derivative of is .

    To find :

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

      2. Apply the power rule: goes to

      The result is:

    Now plug in to the quotient rule:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
    1        log(x) 
--------- - --------
x*(x - 1)          2
            (x - 1) 
$$- \frac{\log{\left(x \right)}}{\left(x - 1\right)^{2}} + \frac{1}{x \left(x - 1\right)}$$
The second derivative [src]
  1        2         2*log(x)
- -- - ---------- + ---------
   2   x*(-1 + x)           2
  x                 (-1 + x) 
-----------------------------
            -1 + x           
$$\frac{\frac{2 \log{\left(x \right)}}{\left(x - 1\right)^{2}} - \frac{2}{x \left(x - 1\right)} - \frac{1}{x^{2}}}{x - 1}$$
The third derivative [src]
2     6*log(x)        3             6     
-- - --------- + ----------- + -----------
 3           3    2                      2
x    (-1 + x)    x *(-1 + x)   x*(-1 + x) 
------------------------------------------
                  -1 + x                  
$$\frac{- \frac{6 \log{\left(x \right)}}{\left(x - 1\right)^{3}} + \frac{6}{x \left(x - 1\right)^{2}} + \frac{3}{x^{2} \left(x - 1\right)} + \frac{2}{x^{3}}}{x - 1}$$
The graph
Derivative of y=(ln*x)/(x-1)