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

Derivative of arcctg(2x*2^(x))

Function f() - derivative -N order at the point
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The solution

You have entered [src] 
    /     x\
acot\2*x*2 /
acot⁡(2x2x)\operatorname{acot}{\left(2^{x} 2 x \right)} 
acot((2*x)*2^x)
The graph
02468-8-6-4-2-10105-5
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
 /   x        x       \ 
-\2*2  + 2*x*2 *log(2)/ 
------------------------
            2*x  2      
     1 + 4*2   *x
−2⋅2xxlog⁡(2)+2⋅2x4⋅22xx2+1- \frac{2 \cdot 2^{x} x \log{\left(2 \right)} + 2 \cdot 2^{x}}{4 \cdot 2^{2 x} x^{2} + 1}
Simplify
The second derivative [src] 
     /                              2*x               2\
   x |                         8*x*2   *(1 + x*log(2)) |
2*2 *|-(2 + x*log(2))*log(2) + ------------------------|
     |                                     2*x  2      |
     \                              1 + 4*2   *x       /
--------------------------------------------------------
                            2*x  2                      
                     1 + 4*2   *x
2⋅2x(8⋅22xx(xlog⁡(2)+1)24⋅22xx2+1−(xlog⁡(2)+2)log⁡(2))4⋅22xx2+1\frac{2 \cdot 2^{x} \left(\frac{8 \cdot 2^{2 x} x \left(x \log{\left(2 \right)} + 1\right)^{2}}{4 \cdot 2^{2 x} x^{2} + 1} - \left(x \log{\left(2 \right)} + 2\right) \log{\left(2 \right)}\right)}{4 \cdot 2^{2 x} x^{2} + 1}
Simplify
The third derivative [src] 
     /                                4*x  2               3      2*x                /       2    2                \         2*x                                     \
   x |     2                     128*2   *x *(1 + x*log(2))    8*2   *(1 + x*log(2))*\1 + 2*x *log (2) + 4*x*log(2)/   16*x*2   *(1 + x*log(2))*(2 + x*log(2))*log(2)|
2*2 *|- log (2)*(3 + x*log(2)) - --------------------------- + ----------------------------------------------------- + ----------------------------------------------|
     |                                                2                                   2*x  2                                              2*x  2                 |
     |                                 /       2*x  2\                             1 + 4*2   *x                                        1 + 4*2   *x                  |
     \                                 \1 + 4*2   *x /                                                                                                               /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                   2*x  2                                                                             
                                                                            1 + 4*2   *x
2⋅2x(−128⋅24xx2(xlog⁡(2)+1)3(4⋅22xx2+1)2+16⋅22xx(xlog⁡(2)+1)(xlog⁡(2)+2)log⁡(2)4⋅22xx2+1+8⋅22x(xlog⁡(2)+1)(2x2log⁡(2)2+4xlog⁡(2)+1)4⋅22xx2+1−(xlog⁡(2)+3)log⁡(2)2)4⋅22xx2+1\frac{2 \cdot 2^{x} \left(- \frac{128 \cdot 2^{4 x} x^{2} \left(x \log{\left(2 \right)} + 1\right)^{3}}{\left(4 \cdot 2^{2 x} x^{2} + 1\right)^{2}} + \frac{16 \cdot 2^{2 x} x \left(x \log{\left(2 \right)} + 1\right) \left(x \log{\left(2 \right)} + 2\right) \log{\left(2 \right)}}{4 \cdot 2^{2 x} x^{2} + 1} + \frac{8 \cdot 2^{2 x} \left(x \log{\left(2 \right)} + 1\right) \left(2 x^{2} \log{\left(2 \right)}^{2} + 4 x \log{\left(2 \right)} + 1\right)}{4 \cdot 2^{2 x} x^{2} + 1} - \left(x \log{\left(2 \right)} + 3\right) \log{\left(2 \right)}^{2}\right)}{4 \cdot 2^{2 x} x^{2} + 1}
Simplify
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