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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

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The solution

You have entered [src] 
   /     3\
log\1 - x /
log⁡(1−x3)\log{\left(1 - x^{3} \right)} 
log(1 - x^3)
Detail solution

  1. Let u=1−x3u = 1 - x^{3}.

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

  3. Then, apply the chain rule. Multiply by ddx(1−x3)\frac{d}{d x} \left(1 - x^{3}\right):

    1. Differentiate 1−x31 - x^{3} term by term:

      1. The derivative of the constant 11 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: x3x^{3} goes to 3x23 x^{2}

        So, the result is: −3x2- 3 x^{2}

      The result is: −3x2- 3 x^{2}

    The result of the chain rule is:

    −3x21−x3- \frac{3 x^{2}}{1 - x^{3}}

  4. Now simplify:

    3x2x3−1\frac{3 x^{2}}{x^{3} - 1}

The answer is:

3x2x3−1\frac{3 x^{2}}{x^{3} - 1}

The graph
02468-8-6-4-2-1010-2020
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
    2 
-3*x  
------
     3
1 - x
−3x21−x3- \frac{3 x^{2}}{1 - x^{3}}
Simplify
The second derivative [src] 
    /         3 \
    |      3*x  |
3*x*|2 - -------|
    |          3|
    \    -1 + x /
-----------------
           3     
     -1 + x
3x(−3x3x3−1+2)x3−1\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
6(9x6(x3−1)2−9x3x3−1+1)x3−1\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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