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Derivative of:
Derivative of 2*cos(3*x)
Derivative of 1^3*sqrt(x)
Derivative of (x+4)/(x-1)
Derivative of (x-3)^4
Graphing y =:
lnx/x^3
Integral of d{x}:
lnx/x^3
Identical expressions
lnx/x^ three
lnx divide by x cubed
lnx divide by x to the power of three
lnx/x3
lnx/x³
lnx/x to the power of 3
lnx divide by x^3

The derivative of the function/ lnx/x^3

Derivative of lnx/x^3

The solution

You have entered [src]

log(x)
------
   3  
  x

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

d /log(x)\
--|------|
dx|   3  |
  \  x   /

$$\frac{d}{d x} \frac{\log{\left(x \right)}}{x^{3}}$$

Transform

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 $g{\left(x \right)} = x^{3}$ .

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: $x^{3}$ goes to $3 x^{2}$
Now plug in to the quotient rule:

$\frac{- 3 x^{2} \log{\left(x \right)} + x^{2}}{x^{6}}$
Now simplify:

$\frac{1 - 3 \log{\left(x \right)}}{x^{4}}$

The answer is:

$\frac{1 - 3 \log{\left(x \right)}}{x^{4}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 1     3*log(x)
---- - --------
   3       4   
x*x       x

$$\frac{1}{x x^{3}} - \frac{3 \log{\left(x \right)}}{x^{4}}$$

Simplify

The second derivative [src]

-7 + 12*log(x)
--------------
       5      
      x

$$\frac{12 \log{\left(x \right)} - 7}{x^{5}}$$

Simplify

The third derivative [src]

47 - 60*log(x)
--------------
       6      
      x

$$\frac{47 - 60 \log{\left(x \right)}}{x^{6}}$$

Simplify

The graph

Derivative of lnx/x^3