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ln^2(x)
The derivative of the function/ ln^2(x)

Derivative of ln^2(x)

Function f() - derivative -N order at the point
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The graph:

from to

Piecewise:

The solution

You have entered [src] 
   2   
log (x)
log⁡(x)2\log{\left(x \right)}^{2} 
log(x)^2
Detail solution

  1. Let u=log⁡(x)u = \log{\left(x \right)}.

  2. Apply the power rule: u2u^{2} goes to 2u2 u

  3. Then, apply the chain rule. Multiply by ddxlog⁡(x)\frac{d}{d x} \log{\left(x \right)}:

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

    The result of the chain rule 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))
--------------
       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 ln^2(x)
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