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Derivative of (2*ln(x)/x)-(1/x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
2*log(x)   1
-------- - -
   x       x
$$\frac{2 \log{\left(x \right)}}{x} - \frac{1}{x}$$
(2*log(x))/x - 1/x
Detail solution
  1. Differentiate term by term:

    1. Apply the quotient rule, which is:

      and .

      To find :

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

        1. The derivative of is .

        So, the result is:

      To find :

      1. Apply the power rule: goes to

      Now plug in to the quotient rule:

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

      1. Apply the power rule: goes to

      So, the result is:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
3    2*log(x)
-- - --------
 2       2   
x       x    
$$- \frac{2 \log{\left(x \right)}}{x^{2}} + \frac{3}{x^{2}}$$
The second derivative [src]
4*(-2 + log(x))
---------------
        3      
       x       
$$\frac{4 \left(\log{\left(x \right)} - 2\right)}{x^{3}}$$
The third derivative [src]
4*(7 - 3*log(x))
----------------
        4       
       x        
$$\frac{4 \left(7 - 3 \log{\left(x \right)}\right)}{x^{4}}$$