Derivative of е^1/lnx

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   1  
  E   
------
log(x)

$$\frac{e^{1}}{\log{\left(x \right)}}$$

E^1/log(x)

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = \log{\left(x \right)}$ .
2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \log{\left(x \right)}$ :
  1. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
  The result of the chain rule is:
  
  $- \frac{1}{x \log{\left(x \right)}^{2}}$
So, the result is: $- \frac{e}{x \log{\left(x \right)}^{2}}$

The answer is:

$- \frac{e}{x \log{\left(x \right)}^{2}}$

The graph

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The first derivative [src]

   -E    
---------
     2   
x*log (x)

$$- \frac{e}{x \log{\left(x \right)}^{2}}$$

Simplify

The second derivative [src]

  /      2   \
E*|1 + ------|
  \    log(x)/
--------------
   2    2     
  x *log (x)

$$\frac{e \left(1 + \frac{2}{\log{\left(x \right)}}\right)}{x^{2} \log{\left(x \right)}^{2}}$$

Simplify

The third derivative [src]

     /      3         3   \
-2*E*|1 + ------ + -------|
     |    log(x)      2   |
     \             log (x)/
---------------------------
          3    2           
         x *log (x)

$$- \frac{2 e \left(1 + \frac{3}{\log{\left(x \right)}} + \frac{3}{\log{\left(x \right)}^{2}}\right)}{x^{3} \log{\left(x \right)}^{2}}$$

Simplify

The graph

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Identical expressions

Derivative of е^1/lnx

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The solution