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Derivative of:
Derivative of 2*x^5
Derivative of y=(x^3-3)(x^2+4x+1)
Derivative of x*e^x+11
Derivative of x*cos(3*x)
Graphing y =:
ln(x)/x^2
Integral of d{x}:
ln(x)/x^2
Identical expressions
ln(x)/x^ two
ln(x) divide by x squared
ln(x) divide by x to the power of two
ln(x)/x2
lnx/x2
ln(x)/x²
ln(x)/x to the power of 2
lnx/x^2
ln(x) divide by x^2

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

Derivative of ln(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 ln(x)/x^2