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ln(1-x^3)
The derivative of the function/ ln(1-x^3)

Derivative of ln(1-x^3)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   /     3\
log\1 - x /
$$\log{\left(1 - x^{3} \right)}$$ 
log(1 - x^3)
Detail solution

  1. Let .

  2. The derivative of is .

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

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

      2. 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 is:

    The result of the chain rule is:

  4. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
    2 
-3*x  
------
     3
1 - x
$$- \frac{3 x^{2}}{1 - x^{3}}$$
Simplify
The second derivative [src] 
    /         3 \
    |      3*x  |
3*x*|2 - -------|
    |          3|
    \    -1 + x /
-----------------
           3     
     -1 + x
$$\frac{3 x \left(- \frac{3 x^{3}}{x^{3} - 1} + 2\right)}{x^{3} - 1}$$
Simplify
The third derivative [src] 
  /         3          6   \
  |      9*x        9*x    |
6*|1 - ------- + ----------|
  |          3            2|
  |    -1 + x    /      3\ |
  \              \-1 + x / /
----------------------------
                3           
          -1 + x
$$\frac{6 \left(\frac{9 x^{6}}{\left(x^{3} - 1\right)^{2}} - \frac{9 x^{3}}{x^{3} - 1} + 1\right)}{x^{3} - 1}$$
Simplify
The graph
Derivative of ln(1-x^3)
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