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3*e^x/log(x)
The derivative of the function/ 3*e^x/log(x)

Derivative of 3*e^x/log(x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
    x 
 3*E  
------
log(x)
3exlog⁡(x)\frac{3 e^{x}}{\log{\left(x \right)}} 
(3*E^x)/log(x)
Detail solution

  1. Apply the quotient rule, which is:

    ddxf(x)g(x)=−f(x)ddxg(x)+g(x)ddxf(x)g2(x)\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}

    f(x)=3exf{\left(x \right)} = 3 e^{x} and g(x)=log⁡(x)g{\left(x \right)} = \log{\left(x \right)}.

    To find ddxf(x)\frac{d}{d x} f{\left(x \right)}:

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

      1. The derivative of exe^{x} is itself.

      So, the result is: 3ex3 e^{x}

    To find ddxg(x)\frac{d}{d x} g{\left(x \right)}:

    1. The derivative of log⁡(x)\log{\left(x \right)} is 1x\frac{1}{x}.

    Now plug in to the quotient rule:

    3exlog⁡(x)−3exxlog⁡(x)2\frac{3 e^{x} \log{\left(x \right)} - \frac{3 e^{x}}{x}}{\log{\left(x \right)}^{2}}

  2. Now simplify:

    3(xlog⁡(x)−1)exxlog⁡(x)2\frac{3 \left(x \log{\left(x \right)} - 1\right) e^{x}}{x \log{\left(x \right)}^{2}}

The answer is:

3(xlog⁡(x)−1)exxlog⁡(x)2\frac{3 \left(x \log{\left(x \right)} - 1\right) e^{x}}{x \log{\left(x \right)}^{2}}

The graph
02468-8-6-4-2-1010-5000050000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
    x          x  
 3*e        3*e   
------ - ---------
log(x)        2   
         x*log (x)
3exlog⁡(x)−3exxlog⁡(x)2\frac{3 e^{x}}{\log{\left(x \right)}} - \frac{3 e^{x}}{x \log{\left(x \right)}^{2}}
Simplify
The second derivative [src] 
  /                     2   \   
  |               1 + ------|   
  |       2           log(x)|  x
3*|1 - -------- + ----------|*e 
  |    x*log(x)    2        |   
  \               x *log(x) /   
--------------------------------
             log(x)
3(1−2xlog⁡(x)+1+2log⁡(x)x2log⁡(x))exlog⁡(x)\frac{3 \left(1 - \frac{2}{x \log{\left(x \right)}} + \frac{1 + \frac{2}{\log{\left(x \right)}}}{x^{2} \log{\left(x \right)}}\right) e^{x}}{\log{\left(x \right)}}
Simplify
The third derivative [src] 
  /                 /      3         3   \                 \   
  |               2*|1 + ------ + -------|     /      2   \|   
  |                 |    log(x)      2   |   3*|1 + ------||   
  |       3         \             log (x)/     \    log(x)/|  x
3*|1 - -------- - ------------------------ + --------------|*e 
  |    x*log(x)           3                     2          |   
  \                      x *log(x)             x *log(x)   /   
---------------------------------------------------------------
                             log(x)
3(1−3xlog⁡(x)+3(1+2log⁡(x))x2log⁡(x)−2(1+3log⁡(x)+3log⁡(x)2)x3log⁡(x))exlog⁡(x)\frac{3 \left(1 - \frac{3}{x \log{\left(x \right)}} + \frac{3 \left(1 + \frac{2}{\log{\left(x \right)}}\right)}{x^{2} \log{\left(x \right)}} - \frac{2 \left(1 + \frac{3}{\log{\left(x \right)}} + \frac{3}{\log{\left(x \right)}^{2}}\right)}{x^{3} \log{\left(x \right)}}\right) e^{x}}{\log{\left(x \right)}}
Simplify
The graph
Derivative of 3*e^x/log(x)
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