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

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

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The solution

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 tan(x)     2   
E      *acot (x)
$$e^{\tan{\left(x \right)}} \operatorname{acot}^{2}{\left(x \right)}$$
E^tan(x)*acot(x)^2
The graph
The first derivative [src]
                                            tan(x)
    2    /       2   \  tan(x)   2*acot(x)*e      
acot (x)*\1 + tan (x)/*e       - -----------------
                                            2     
                                       1 + x      
$$\left(\tan^{2}{\left(x \right)} + 1\right) e^{\tan{\left(x \right)}} \operatorname{acot}^{2}{\left(x \right)} - \frac{2 e^{\tan{\left(x \right)}} \operatorname{acot}{\left(x \right)}}{x^{2} + 1}$$
The second derivative [src]
/                                                                          /       2   \        \        
|2*(1 + 2*x*acot(x))       2    /       2   \ /       2              \   4*\1 + tan (x)/*acot(x)|  tan(x)
|------------------- + acot (x)*\1 + tan (x)/*\1 + tan (x) + 2*tan(x)/ - -----------------------|*e      
|             2                                                                        2        |        
|     /     2\                                                                    1 + x         |        
\     \1 + x /                                                                                  /        
$$\left(\left(\tan^{2}{\left(x \right)} + 1\right) \left(\tan^{2}{\left(x \right)} + 2 \tan{\left(x \right)} + 1\right) \operatorname{acot}^{2}{\left(x \right)} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right) \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + \frac{2 \left(2 x \operatorname{acot}{\left(x \right)} + 1\right)}{\left(x^{2} + 1\right)^{2}}\right) e^{\tan{\left(x \right)}}$$
The third derivative [src]
/    /                       2        \                                                                                                                                                                          \        
|    |            3*x     4*x *acot(x)|                                                                                                                                                                          |        
|  4*|-acot(x) + ------ + ------------|                                                                                                                                                                          |        
|    |                2           2   |                          /                 2                                     \     /       2   \                       /       2   \ /       2              \        |        
|    \           1 + x       1 + x    /       2    /       2   \ |    /       2   \         2        /       2   \       |   6*\1 + tan (x)/*(1 + 2*x*acot(x))   6*\1 + tan (x)/*\1 + tan (x) + 2*tan(x)/*acot(x)|  tan(x)
|- ------------------------------------ + acot (x)*\1 + tan (x)/*\2 + \1 + tan (x)/  + 6*tan (x) + 6*\1 + tan (x)/*tan(x)/ + --------------------------------- - ------------------------------------------------|*e      
|                       2                                                                                                                        2                                         2                     |        
|               /     2\                                                                                                                 /     2\                                     1 + x                      |        
\               \1 + x /                                                                                                                 \1 + x /                                                                /        
$$\left(\left(\tan^{2}{\left(x \right)} + 1\right) \left(\left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 6 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + 6 \tan^{2}{\left(x \right)} + 2\right) \operatorname{acot}^{2}{\left(x \right)} - \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \left(\tan^{2}{\left(x \right)} + 2 \tan{\left(x \right)} + 1\right) \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + \frac{6 \left(2 x \operatorname{acot}{\left(x \right)} + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(x^{2} + 1\right)^{2}} - \frac{4 \left(\frac{4 x^{2} \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + \frac{3 x}{x^{2} + 1} - \operatorname{acot}{\left(x \right)}\right)}{\left(x^{2} + 1\right)^{2}}\right) e^{\tan{\left(x \right)}}$$