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

Derivative of ln^3(3x)

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

The graph:

from to

Piecewise:

The solution

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

  1. Let .

  2. Apply the power rule: goes to

  3. Then, apply the chain rule. Multiply by :

    1. Let .

    2. The derivative of is .

    3. Then, apply the chain rule. Multiply by :

      1. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

      The result of the chain rule is:

    The result of the chain rule is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     2     
3*log (3*x)
-----------
     x
$$\frac{3 \log{\left(3 x \right)}^{2}}{x}$$
Simplify
The second derivative [src] 
3*(2 - log(3*x))*log(3*x)
-------------------------
             2           
            x
$$\frac{3 \left(2 - \log{\left(3 x \right)}\right) \log{\left(3 x \right)}}{x^{2}}$$
Simplify
The third derivative [src] 
  /       2                  \
6*\1 + log (3*x) - 3*log(3*x)/
------------------------------
               3              
              x
$$\frac{6 \left(\log{\left(3 x \right)}^{2} - 3 \log{\left(3 x \right)} + 1\right)}{x^{3}}$$
Simplify
The graph
Derivative of ln^3(3x)
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