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y/(ln(y)-1)
The derivative of the function/ y/(ln(y)-1)

Derivative of y/(ln(y)-1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
    y     
----------
log(y) - 1
$$\frac{y}{\log{\left(y \right)} - 1}$$ 
y/(log(y) - 1)
Detail solution

  1. Apply the quotient rule, which is:

    and .

    To find :

    1. Apply the power rule: goes to

    To find :

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

      2. The derivative of is .

      The result is:

    Now plug in to the quotient rule:

The answer is:

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