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log(x)/x
The derivative of the function/ log(x)/x

Derivative of log(x)/x

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

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from to

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The solution

You have entered [src] 
log(x)
------
  x
log⁡(x)x\frac{\log{\left(x \right)}}{x} 
d /log(x)\
--|------|
dx\  x   /
ddxlog⁡(x)x\frac{d}{d x} \frac{\log{\left(x \right)}}{x}
Transform
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)=log⁡(x)f{\left(x \right)} = \log{\left(x \right)} and g(x)=xg{\left(x \right)} = x.

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

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

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

    1. Apply the power rule: xx goes to 11

    Now plug in to the quotient rule:

    1−log⁡(x)x2\frac{1 - \log{\left(x \right)}}{x^{2}}

The answer is:

1−log⁡(x)x2\frac{1 - \log{\left(x \right)}}{x^{2}}

The graph
02468-8-6-4-2-1010-500500
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
1    log(x)
-- - ------
 2      2  
x      x
−log⁡(x)x2+1x2- \frac{\log{\left(x \right)}}{x^{2}} + \frac{1}{x^{2}}
Simplify
The second derivative [src] 
-3 + 2*log(x)
-------------
       3     
      x
2log⁡(x)−3x3\frac{2 \log{\left(x \right)} - 3}{x^{3}}
Simplify
The third derivative [src] 
11 - 6*log(x)
-------------
       4     
      x
11−6log⁡(x)x4\frac{11 - 6 \log{\left(x \right)}}{x^{4}}
Simplify
The graph
Derivative of log(x)/x
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