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sqrt(x)*log(x)
The derivative of the function/ sqrt(x)*log(x)

Derivative of sqrt(x)*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)
xlog⁡(x)\sqrt{x} \log{\left(x \right)} 
sqrt(x)*log(x)
Detail solution

  1. Apply the product rule:

    ddxf(x)g(x)=f(x)ddxg(x)+g(x)ddxf(x)\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}

    f(x)=xf{\left(x \right)} = \sqrt{x}; to find ddxf(x)\frac{d}{d x} f{\left(x \right)}:

    1. Apply the power rule: x\sqrt{x} goes to 12x\frac{1}{2 \sqrt{x}}

    g(x)=log⁡(x)g{\left(x \right)} = \log{\left(x \right)}; to find ddxg(x)\frac{d}{d x} g{\left(x \right)}:

    1. The derivative of log⁡(x)\log{\left(x \right)} is 1x\frac{1}{x}.

    The result is: log⁡(x)2x+1x\frac{\log{\left(x \right)}}{2 \sqrt{x}} + \frac{1}{\sqrt{x}}

  2. Now simplify:

    log⁡(x)+22x\frac{\log{\left(x \right)} + 2}{2 \sqrt{x}}

The answer is:

log⁡(x)+22x\frac{\log{\left(x \right)} + 2}{2 \sqrt{x}}

The graph
02468-8-6-4-2-1010-1010
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  1      log(x)
----- + -------
  ___       ___
\/ x    2*\/ x
log⁡(x)2x+1x\frac{\log{\left(x \right)}}{2 \sqrt{x}} + \frac{1}{\sqrt{x}}
Simplify
The second derivative [src] 
-log(x) 
--------
    3/2 
 4*x
−log⁡(x)4x32- \frac{\log{\left(x \right)}}{4 x^{\frac{3}{2}}}
Simplify
The third derivative [src] 
-2 + 3*log(x)
-------------
       5/2   
    8*x
3log⁡(x)−28x52\frac{3 \log{\left(x \right)} - 2}{8 x^{\frac{5}{2}}}
Simplify
The graph
Derivative of sqrt(x)*log(x)
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