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x^(1/2)*log(x)

Derivative of x^(1/2)*log(x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
  ___       
\/ x *log(x)
$$\sqrt{x} \log{\left(x \right)}$$
sqrt(x)*log(x)
Detail solution
  1. Apply the product rule:

    ; to find :

    1. Apply the power rule: goes to

    ; to find :

    1. The derivative of is .

    The result is:

  2. Now simplify:


The answer is:

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