Mister Exam

Derivative of log(x)/sqrt(x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
log(x)
------
  ___ 
\/ x  
$$\frac{\log{\left(x \right)}}{\sqrt{x}}$$
d /log(x)\
--|------|
dx|  ___ |
  \\/ x  /
$$\frac{d}{d x} \frac{\log{\left(x \right)}}{\sqrt{x}}$$
Detail solution
  1. Apply the quotient rule, which is:

    and .

    To find :

    1. The derivative of is .

    To find :

    1. Apply the power rule: goes to

    Now plug in to the quotient rule:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
   1      log(x)
------- - ------
    ___      3/2
x*\/ x    2*x   
$$\frac{1}{\sqrt{x} x} - \frac{\log{\left(x \right)}}{2 x^{\frac{3}{2}}}$$
The second derivative [src]
     3*log(x)
-2 + --------
        4    
-------------
      5/2    
     x       
$$\frac{\frac{3 \log{\left(x \right)}}{4} - 2}{x^{\frac{5}{2}}}$$
The third derivative [src]
46 - 15*log(x)
--------------
       7/2    
    8*x       
$$\frac{46 - 15 \log{\left(x \right)}}{8 x^{\frac{7}{2}}}$$
The graph
Derivative of log(x)/sqrt(x)