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Derivative of arctg(x/4)-((x-3)/(2-2x))

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

The graph:

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The solution

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