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

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

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

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The solution

You have entered [src] 
 tan(x)     2   
E      *acot (x)
etan⁡(x)acot⁡2(x)e^{\tan{\left(x \right)}} \operatorname{acot}^{2}{\left(x \right)} 
E^tan(x)*acot(x)^2
The graph
02468-8-6-4-2-1010-100000000000000100000000000000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
                                            tan(x)
    2    /       2   \  tan(x)   2*acot(x)*e      
acot (x)*\1 + tan (x)/*e       - -----------------
                                            2     
                                       1 + x
(tan⁡2(x)+1)etan⁡(x)acot⁡2(x)−2etan⁡(x)acot⁡(x)x2+1\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}
Simplify
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 /                                                                                  /
((tan⁡2(x)+1)(tan⁡2(x)+2tan⁡(x)+1)acot⁡2(x)−4(tan⁡2(x)+1)acot⁡(x)x2+1+2(2xacot⁡(x)+1)(x2+1)2)etan⁡(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)}}
Simplify
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 /                                                                /
((tan⁡2(x)+1)((tan⁡2(x)+1)2+6(tan⁡2(x)+1)tan⁡(x)+6tan⁡2(x)+2)acot⁡2(x)−6(tan⁡2(x)+1)(tan⁡2(x)+2tan⁡(x)+1)acot⁡(x)x2+1+6(2xacot⁡(x)+1)(tan⁡2(x)+1)(x2+1)2−4(4x2acot⁡(x)x2+1+3xx2+1−acot⁡(x))(x2+1)2)etan⁡(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)}}
Simplify
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