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The derivative of the function/ arctan(2*x-(2^x))

Derivative of arctan(2*x-(2^x))

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

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The solution

You have entered [src] 
    /       x\
atan\2*x - 2 /
atan⁡(−2x+2x)\operatorname{atan}{\left(- 2^{x} + 2 x \right)} 
atan(2*x - 2^x)
The graph
02468-8-6-4-2-10102.5-2.5
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
      x        
 2 - 2 *log(2) 
---------------
              2
    /       x\ 
1 + \2*x - 2 /
−2xlog⁡(2)+2(−2x+2x)2+1\frac{- 2^{x} \log{\left(2 \right)} + 2}{\left(- 2^{x} + 2 x\right)^{2} + 1}
Simplify
The second derivative [src] 
                                 2           
                 /      x       \  / x      \
   x    2      2*\-2 + 2 *log(2)/ *\2  - 2*x/
- 2 *log (2) + ------------------------------
                                    2        
                          / x      \         
                      1 + \2  - 2*x/         
---------------------------------------------
                             2               
                   / x      \                
               1 + \2  - 2*x/
−2xlog⁡(2)2+2(2x−2x)(2xlog⁡(2)−2)2(2x−2x)2+1(2x−2x)2+1\frac{- 2^{x} \log{\left(2 \right)}^{2} + \frac{2 \left(2^{x} - 2 x\right) \left(2^{x} \log{\left(2 \right)} - 2\right)^{2}}{\left(2^{x} - 2 x\right)^{2} + 1}}{\left(2^{x} - 2 x\right)^{2} + 1}
Simplify
The third derivative [src] 
                                 3                     3           2                                           
                 /      x       \      /      x       \  / x      \       x    2    /      x       \ / x      \
   x    3      2*\-2 + 2 *log(2)/    8*\-2 + 2 *log(2)/ *\2  - 2*x/    6*2 *log (2)*\-2 + 2 *log(2)/*\2  - 2*x/
- 2 *log (2) + ------------------- - ------------------------------- + ----------------------------------------
                               2                             2                                   2             
                     / x      \             /              2\                          / x      \              
                 1 + \2  - 2*x/             |    / x      \ |                      1 + \2  - 2*x/              
                                            \1 + \2  - 2*x/ /                                                  
---------------------------------------------------------------------------------------------------------------
                                                              2                                                
                                                    / x      \                                                 
                                                1 + \2  - 2*x/
6⋅2x(2x−2x)(2xlog⁡(2)−2)log⁡(2)2(2x−2x)2+1−2xlog⁡(2)3−8(2x−2x)2(2xlog⁡(2)−2)3((2x−2x)2+1)2+2(2xlog⁡(2)−2)3(2x−2x)2+1(2x−2x)2+1\frac{\frac{6 \cdot 2^{x} \left(2^{x} - 2 x\right) \left(2^{x} \log{\left(2 \right)} - 2\right) \log{\left(2 \right)}^{2}}{\left(2^{x} - 2 x\right)^{2} + 1} - 2^{x} \log{\left(2 \right)}^{3} - \frac{8 \left(2^{x} - 2 x\right)^{2} \left(2^{x} \log{\left(2 \right)} - 2\right)^{3}}{\left(\left(2^{x} - 2 x\right)^{2} + 1\right)^{2}} + \frac{2 \left(2^{x} \log{\left(2 \right)} - 2\right)^{3}}{\left(2^{x} - 2 x\right)^{2} + 1}}{\left(2^{x} - 2 x\right)^{2} + 1}
Simplify
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