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ln^3x
The derivative of the function/ ln^3x

Derivative of ln^3x

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   3   
log (x)
log⁡(x)3\log{\left(x \right)}^{3} 
log(x)^3
Detail solution

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

  2. Apply the power rule: u3u^{3} goes to 3u23 u^{2}

  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:

    3log⁡(x)2x\frac{3 \log{\left(x \right)}^{2}}{x}

The answer is:

3log⁡(x)2x\frac{3 \log{\left(x \right)}^{2}}{x}

The graph
02468-8-6-4-2-1010-200200
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     2   
3*log (x)
---------
    x
3log⁡(x)2x\frac{3 \log{\left(x \right)}^{2}}{x}
Simplify
The second derivative [src] 
3*(2 - log(x))*log(x)
---------------------
           2         
          x
3(2−log⁡(x))log⁡(x)x2\frac{3 \left(2 - \log{\left(x \right)}\right) \log{\left(x \right)}}{x^{2}}
Simplify
The third derivative [src] 
  /       2              \
6*\1 + log (x) - 3*log(x)/
--------------------------
             3            
            x
6(log⁡(x)2−3log⁡(x)+1)x3\frac{6 \left(\log{\left(x \right)}^{2} - 3 \log{\left(x \right)} + 1\right)}{x^{3}}
Simplify
The graph
Derivative of ln^3x
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