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Derivative of:
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Limit of the function:
log(x)/x^2
Integral of d{x}:
log(x)/x^2
Identical expressions
log(x)/x^ two
logarithm of (x) divide by x squared
logarithm of (x) divide by x to the power of two
log(x)/x2
logx/x2
log(x)/x²
log(x)/x to the power of 2
logx/x^2
log(x) divide by x^2

The derivative of the function/ log(x)/x^2

Derivative of log(x)/x^2

The solution

You have entered [src]

log(x)
------
   2  
  x

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

log(x)/x^2

Detail solution

Apply the quotient rule, which is:

$\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$

$f{\left(x \right)} = \log{\left(x \right)}$ and $g{\left(x \right)} = x^{2}$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Apply the power rule: $x^{2}$ goes to $2 x$
Now plug in to the quotient rule:

$\frac{- 2 x \log{\left(x \right)} + x}{x^{4}}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 1     2*log(x)
---- - --------
   2       3   
x*x       x

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

Simplify

The second derivative [src]

-5 + 6*log(x)
-------------
       4     
      x

\frac{6 \log{\left(x \right)} - 5}{x^{4}}

Simplify

The third derivative [src]

2*(13 - 12*log(x))
------------------
         5        
        x

\frac{2 \left(13 - 12 \log{\left(x \right)}\right)}{x^{5}}

Simplify

The graph

Derivative of log(x)/x^2