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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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