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Derivative of acos(2^(x-1))

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
    / x - 1\
acos\2     /
$$\operatorname{acos}{\left(2^{x - 1} \right)}$$
acos(2^(x - 1))
The graph
The first derivative [src]
   x - 1          
 -2     *log(2)   
------------------
   _______________
  /      -2 + 2*x 
\/  1 - 2         
$$- \frac{2^{x - 1} \log{\left(2 \right)}}{\sqrt{1 - 2^{2 x - 2}}}$$
The second derivative [src]
            /       2*x  \ 
  x    2    |      2     | 
-2 *log (2)*|4 + --------| 
            |         2*x| 
            |        2   | 
            |    1 - ----| 
            \         4  / 
---------------------------
            __________     
           /      2*x      
          /      2         
     8*  /   1 - ----      
       \/         4        
$$- \frac{2^{x} \left(\frac{2^{2 x}}{1 - \frac{2^{2 x}}{4}} + 4\right) \log{\left(2 \right)}^{2}}{8 \sqrt{1 - \frac{2^{2 x}}{4}}}$$
The third derivative [src]
            /           4*x         2*x \ 
  x    3    |        3*2        16*2    | 
-2 *log (2)*|16 + ----------- + --------| 
            |               2        2*x| 
            |     /     2*x\        2   | 
            |     |    2   |    1 - ----| 
            |     |1 - ----|         4  | 
            \     \     4  /            / 
------------------------------------------
                    __________            
                   /      2*x             
                  /      2                
            32*  /   1 - ----             
               \/         4               
$$- \frac{2^{x} \left(\frac{3 \cdot 2^{4 x}}{\left(1 - \frac{2^{2 x}}{4}\right)^{2}} + \frac{16 \cdot 2^{2 x}}{1 - \frac{2^{2 x}}{4}} + 16\right) \log{\left(2 \right)}^{3}}{32 \sqrt{1 - \frac{2^{2 x}}{4}}}$$