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The derivative of the function/ arccos(ln((2x+1)/3))

Derivative of arccos(ln((2x+1)/3))

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

The graph:

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The solution

You have entered [src] 
    /   /2*x + 1\\
acos|log|-------||
    \   \   3   //
acos⁡(log⁡(2x+13))\operatorname{acos}{\left(\log{\left(\frac{2 x + 1}{3} \right)} \right)} 
acos(log((2*x + 1)/3))
The graph
02468-8-6-4-2-10105-5
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
               -2                
---------------------------------
    ___________________          
   /        2/2*x + 1\           
  /  1 - log |-------| *(2*x + 1)
\/           \   3   /
−21−log⁡(2x+13)2(2x+1)- \frac{2}{\sqrt{1 - \log{\left(\frac{2 x + 1}{3} \right)}^{2}} \left(2 x + 1\right)}
Simplify
The second derivative [src] 
      /          /1 + 2*x\  \     
      |       log|-------|  |     
      |          \   3   /  |     
    4*|1 - -----------------|     
      |           2/1 + 2*x\|     
      |    1 - log |-------||     
      \            \   3   //     
----------------------------------
    ___________________           
   /        2/1 + 2*x\           2
  /  1 - log |-------| *(1 + 2*x) 
\/           \   3   /
4(1−log⁡(2x+13)1−log⁡(2x+13)2)1−log⁡(2x+13)2(2x+1)2\frac{4 \left(1 - \frac{\log{\left(\frac{2 x + 1}{3} \right)}}{1 - \log{\left(\frac{2 x + 1}{3} \right)}^{2}}\right)}{\sqrt{1 - \log{\left(\frac{2 x + 1}{3} \right)}^{2}} \left(2 x + 1\right)^{2}}
Simplify
The third derivative [src] 
  /                                2/1 + 2*x\             /1 + 2*x\ \
  |                           3*log |-------|        3*log|-------| |
  |             1                   \   3   /             \   3   / |
8*|-2 - ----------------- - -------------------- + -----------------|
  |            2/1 + 2*x\                      2          2/1 + 2*x\|
  |     1 - log |-------|   /       2/1 + 2*x\\    1 - log |-------||
  |             \   3   /   |1 - log |-------||            \   3   /|
  \                         \        \   3   //                     /
---------------------------------------------------------------------
                      ___________________                            
                     /        2/1 + 2*x\           3                 
                    /  1 - log |-------| *(1 + 2*x)                  
                  \/           \   3   /
8(−2+3log⁡(2x+13)1−log⁡(2x+13)2−11−log⁡(2x+13)2−3log⁡(2x+13)2(1−log⁡(2x+13)2)2)1−log⁡(2x+13)2(2x+1)3\frac{8 \left(-2 + \frac{3 \log{\left(\frac{2 x + 1}{3} \right)}}{1 - \log{\left(\frac{2 x + 1}{3} \right)}^{2}} - \frac{1}{1 - \log{\left(\frac{2 x + 1}{3} \right)}^{2}} - \frac{3 \log{\left(\frac{2 x + 1}{3} \right)}^{2}}{\left(1 - \log{\left(\frac{2 x + 1}{3} \right)}^{2}\right)^{2}}\right)}{\sqrt{1 - \log{\left(\frac{2 x + 1}{3} \right)}^{2}} \left(2 x + 1\right)^{3}}
Simplify
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