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lnlnx
The derivative of the function/ lnlnx

Derivative of lnlnx

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
log(x)*log(x)
log⁡(x)log⁡(x)\log{\left(x \right)} \log{\left(x \right)} 
log(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)=log⁡(x)f{\left(x \right)} = \log{\left(x \right)}; to find ddxf(x)\frac{d}{d x} f{\left(x \right)}:

    1. The derivative of log⁡(x)\log{\left(x \right)} is 1x\frac{1}{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: 2log⁡(x)x\frac{2 \log{\left(x \right)}}{x}

The answer is:

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

The graph
02468-8-6-4-2-1010-5050
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
2*log(x)
--------
   x
2log⁡(x)x\frac{2 \log{\left(x \right)}}{x}
Simplify
The second derivative [src] 
2*(1 - log(x))
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       2      
      x
2(1−log⁡(x))x2\frac{2 \left(1 - \log{\left(x \right)}\right)}{x^{2}}
Simplify
The third derivative [src] 
2*(-3 + 2*log(x))
-----------------
         3       
        x
2(2log⁡(x)−3)x3\frac{2 \left(2 \log{\left(x \right)} - 3\right)}{x^{3}}
Simplify
The graph
Derivative of lnlnx
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