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y=2(x/lnx)
The derivative of the function/ y=2(x/lnx)

Derivative of y=2(x/lnx)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 2*x  
------
log(x)
$$\frac{2 x}{\log{\left(x \right)}}$$ 
d / 2*x  \
--|------|
dx\log(x)/
$$\frac{d}{d x} \frac{2 x}{\log{\left(x \right)}}$$
Transform
Detail solution

  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Apply the quotient rule, which is:

      and .

      To find :

      1. Apply the power rule: goes to

      To find :

      1. The derivative of is .

      Now plug in to the quotient rule:

    So, the result is:

The answer is:

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