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(пarctanx)/arcctgx
Derivada de la función/ arctan/ (пarctanx)/arcctgx

Derivada de (пarctanx)/arcctgx

Función f() - derivada -er orden en el punto
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
pi*atan(x)
----------
 acot(x)
πatan⁡(x)acot⁡(x)\frac{\pi \operatorname{atan}{\left(x \right)}}{\operatorname{acot}{\left(x \right)}} 
(pi*atan(x))/acot(x)
Gráfica
02468-8-6-4-2-1010-5050
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Trazar el gráfico f'(x)
Primera derivada [src] 
       pi              pi*atan(x)   
---------------- + -----------------
/     2\           /     2\     2   
\1 + x /*acot(x)   \1 + x /*acot (x)
π(x2+1)acot⁡(x)+πatan⁡(x)(x2+1)acot⁡2(x)\frac{\pi}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} + \frac{\pi \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}}
Simplificar
Segunda derivada [src] 
     /              /       1   \        \
     |              |x - -------|*atan(x)|
     |   1          \    acot(x)/        |
2*pi*|------- - x - ---------------------|
     \acot(x)              acot(x)       /
------------------------------------------
                    2                     
            /     2\                      
            \1 + x / *acot(x)
2π(−x−(x−1acot⁡(x))atan⁡(x)acot⁡(x)+1acot⁡(x))(x2+1)2acot⁡(x)\frac{2 \pi \left(- x - \frac{\left(x - \frac{1}{\operatorname{acot}{\left(x \right)}}\right) \operatorname{atan}{\left(x \right)}}{\operatorname{acot}{\left(x \right)}} + \frac{1}{\operatorname{acot}{\left(x \right)}}\right)}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}}
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Tercera derivada [src] 
     /              /                             2                    \                                              \
     |              |             3            4*x           6*x       |                                              |
     |              |-1 + ----------------- + ------ - ----------------|*atan(x)                        /       1   \ |
     |         2    |     /     2\     2           2   /     2\        |                              3*|x - -------| |
     |      4*x     \     \1 + x /*acot (x)   1 + x    \1 + x /*acot(x)/                 3*x            \    acot(x)/ |
2*pi*|-1 + ------ + ------------------------------------------------------------ - ---------------- - ----------------|
     |          2                             acot(x)                              /     2\           /     2\        |
     \     1 + x                                                                   \1 + x /*acot(x)   \1 + x /*acot(x)/
-----------------------------------------------------------------------------------------------------------------------
                                                           2                                                           
                                                   /     2\                                                            
                                                   \1 + x / *acot(x)
2π(4x2x2+1−3x(x2+1)acot⁡(x)−3(x−1acot⁡(x))(x2+1)acot⁡(x)+(4x2x2+1−6x(x2+1)acot⁡(x)−1+3(x2+1)acot⁡2(x))atan⁡(x)acot⁡(x)−1)(x2+1)2acot⁡(x)\frac{2 \pi \left(\frac{4 x^{2}}{x^{2} + 1} - \frac{3 x}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} - \frac{3 \left(x - \frac{1}{\operatorname{acot}{\left(x \right)}}\right)}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} + \frac{\left(\frac{4 x^{2}}{x^{2} + 1} - \frac{6 x}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} - 1 + \frac{3}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}}\right) \operatorname{atan}{\left(x \right)}}{\operatorname{acot}{\left(x \right)}} - 1\right)}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}}
Simplificar
Gráfico
Derivada de (пarctanx)/arcctgx
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