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Similar expressions
log(1/sqrt(1+x^4))/log2

The derivative of the function/ log(1/sqrt(1-x^4))/log2

Derivative of log(1/sqrt(1-x^4))/log2

The solution

You have entered [src]

   /     1     \
log|-----------|
   |   ________|
   |  /      4 |
   \\/  1 - x  /
----------------
     log(2)

$$\frac{\log{\left(\frac{1}{\sqrt{1 - x^{4}}} \right)}}{\log{\left(2 \right)}}$$

log(1/(sqrt(1 - x^4)))/log(2)

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = \frac{1}{\sqrt{1 - x^{4}}}$ .
2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \frac{1}{\sqrt{1 - x^{4}}}$ :
  1. Let $u = \sqrt{1 - x^{4}}$ .
  2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \sqrt{1 - x^{4}}$ :
    1. Let $u = 1 - x^{4}$ .
    2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
    3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(1 - x^{4}\right)$ :
      1. Differentiate $1 - x^{4}$ term by term:
        
        The derivative of the constant $1$ is zero.
        
        The derivative of a constant times a function is the constant times the derivative of the function.
        
        Apply the power rule: $x^{4}$ goes to $4 x^{3}$
        
        So, the result is: $- 4 x^{3}$
        
        The result is: $- 4 x^{3}$
      The result of the chain rule is:
      
      $- \frac{2 x^{3}}{\sqrt{1 - x^{4}}}$
    The result of the chain rule is:
    
    $\frac{2 x^{3}}{\left(1 - x^{4}\right)^{\frac{3}{2}}}$
  The result of the chain rule is:
  
  $\frac{2 x^{3}}{1 - x^{4}}$
So, the result is: $\frac{2 x^{3}}{\left(1 - x^{4}\right) \log{\left(2 \right)}}$
Now simplify:

$- \frac{2 x^{3}}{\left(x^{4} - 1\right) \log{\left(2 \right)}}$

The answer is:

$- \frac{2 x^{3}}{\left(x^{4} - 1\right) \log{\left(2 \right)}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

         3     
      2*x      
---------------
/     4\       
\1 - x /*log(2)

$$\frac{2 x^{3}}{\left(1 - x^{4}\right) \log{\left(2 \right)}}$$

Simplify

The second derivative [src]

     /          4 \
   2 |       4*x  |
2*x *|-3 + -------|
     |           4|
     \     -1 + x /
-------------------
  /      4\        
  \-1 + x /*log(2)

$$\frac{2 x^{2} \left(\frac{4 x^{4}}{x^{4} - 1} - 3\right)}{\left(x^{4} - 1\right) \log{\left(2 \right)}}$$

Simplify

The third derivative [src]

     /         4          8   \
     |     18*x       16*x    |
-4*x*|3 - ------- + ----------|
     |          4            2|
     |    -1 + x    /      4\ |
     \              \-1 + x / /
-------------------------------
        /      4\              
        \-1 + x /*log(2)

$$- \frac{4 x \left(\frac{16 x^{8}}{\left(x^{4} - 1\right)^{2}} - \frac{18 x^{4}}{x^{4} - 1} + 3\right)}{\left(x^{4} - 1\right) \log{\left(2 \right)}}$$

Simplify

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Derivative of log(1/sqrt(1-x^4))/log2

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The solution