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y=arctancsch(cotx)
Derivada de la función/ arctan/ y=arctancsch(cotx)

Derivada de y=arctancsch(cotx)

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
atan(csch(cot(x)))
atan⁡(csch⁡(cot⁡(x)))\operatorname{atan}{\left(\operatorname{csch}{\left(\cot{\left(x \right)} \right)} \right)} 
atan(csch(cot(x)))
Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
 /        2   \                           
-\-1 - cot (x)/*coth(cot(x))*csch(cot(x)) 
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                    2                     
            1 + csch (cot(x))
−(−cot⁡2(x)−1)coth⁡(cot⁡(x))csch⁡(cot⁡(x))csch⁡2(cot⁡(x))+1- \frac{\left(- \cot^{2}{\left(x \right)} - 1\right) \coth{\left(\cot{\left(x \right)} \right)} \operatorname{csch}{\left(\cot{\left(x \right)} \right)}}{\operatorname{csch}^{2}{\left(\cot{\left(x \right)} \right)} + 1}
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Segunda derivada [src] 
              /                                      2                                     2             2         /       2   \\             
/       2   \ |    2         /       2   \    1 + cot (x)                            2*coth (cot(x))*csch (cot(x))*\1 + cot (x)/|             
\1 + cot (x)/*|coth (cot(x))*\1 + cot (x)/ + ------------- - 2*cot(x)*coth(cot(x)) - -------------------------------------------|*csch(cot(x))
              |                                  2                                                        2                     |             
              \                              sinh (cot(x))                                        1 + csch (cot(x))             /             
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                                                                      2                                                                       
                                                              1 + csch (cot(x))
(cot⁡2(x)+1)((cot⁡2(x)+1)coth⁡2(cot⁡(x))+cot⁡2(x)+1sinh⁡2(cot⁡(x))−2(cot⁡2(x)+1)coth⁡2(cot⁡(x))csch⁡2(cot⁡(x))csch⁡2(cot⁡(x))+1−2cot⁡(x)coth⁡(cot⁡(x)))csch⁡(cot⁡(x))csch⁡2(cot⁡(x))+1\frac{\left(\cot^{2}{\left(x \right)} + 1\right) \left(\left(\cot^{2}{\left(x \right)} + 1\right) \coth^{2}{\left(\cot{\left(x \right)} \right)} + \frac{\cot^{2}{\left(x \right)} + 1}{\sinh^{2}{\left(\cot{\left(x \right)} \right)}} - \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right) \coth^{2}{\left(\cot{\left(x \right)} \right)} \operatorname{csch}^{2}{\left(\cot{\left(x \right)} \right)}}{\operatorname{csch}^{2}{\left(\cot{\left(x \right)} \right)} + 1} - 2 \cot{\left(x \right)} \coth{\left(\cot{\left(x \right)} \right)}\right) \operatorname{csch}{\left(\cot{\left(x \right)} \right)}}{\operatorname{csch}^{2}{\left(\cot{\left(x \right)} \right)} + 1}
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Tercera derivada [src] 
              /                                                                                                                                                                      2                               2                               2                                              2                                              2                                                                                 \             
              |             2                                                                                                                  /       2   \            /       2   \                   /       2   \                   /       2   \      3             2             /       2   \      3             4             /       2   \      2                               2             2         /       2   \       |             
/       2   \ |/       2   \      3             /       2   \                     2                         2         /       2   \          6*\1 + cot (x)/*cot(x)   2*\1 + cot (x)/ *cosh(cot(x))   3*\1 + cot (x)/ *coth(cot(x))   8*\1 + cot (x)/ *coth (cot(x))*csch (cot(x))   8*\1 + cot (x)/ *coth (cot(x))*csch (cot(x))   6*\1 + cot (x)/ *csch (cot(x))*coth(cot(x))   12*coth (cot(x))*csch (cot(x))*\1 + cot (x)/*cot(x)|             
\1 + cot (x)/*|\1 + cot (x)/ *coth (cot(x)) + 2*\1 + cot (x)/*coth(cot(x)) + 4*cot (x)*coth(cot(x)) - 6*coth (cot(x))*\1 + cot (x)/*cot(x) - ---------------------- + ----------------------------- + ----------------------------- - -------------------------------------------- + -------------------------------------------- - ------------------------------------------- + ---------------------------------------------------|*csch(cot(x))
              |                                                                                                                                      2                            3                               2                                        2                                                        2                    /        2        \     2                                         2                         |             
              |                                                                                                                                  sinh (cot(x))                sinh (cot(x))                   sinh (cot(x))                        1 + csch (cot(x))                             /        2        \                     \1 + csch (cot(x))/*sinh (cot(x))                         1 + csch (cot(x))                 |             
              \                                                                                                                                                                                                                                                                                  \1 + csch (cot(x))/                                                                                                                 /             
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                                                                                                                                                                                                                         2                                                                                                                                                                                                                         
                                                                                                                                                                                                                 1 + csch (cot(x))
(cot⁡2(x)+1)((cot⁡2(x)+1)2coth⁡3(cot⁡(x))+3(cot⁡2(x)+1)2coth⁡(cot⁡(x))sinh⁡2(cot⁡(x))+2(cot⁡2(x)+1)2cosh⁡(cot⁡(x))sinh⁡3(cot⁡(x))−8(cot⁡2(x)+1)2coth⁡3(cot⁡(x))csch⁡2(cot⁡(x))csch⁡2(cot⁡(x))+1−6(cot⁡2(x)+1)2coth⁡(cot⁡(x))csch⁡2(cot⁡(x))(csch⁡2(cot⁡(x))+1)sinh⁡2(cot⁡(x))+8(cot⁡2(x)+1)2coth⁡3(cot⁡(x))csch⁡4(cot⁡(x))(csch⁡2(cot⁡(x))+1)2−6(cot⁡2(x)+1)cot⁡(x)coth⁡2(cot⁡(x))−6(cot⁡2(x)+1)cot⁡(x)sinh⁡2(cot⁡(x))+2(cot⁡2(x)+1)coth⁡(cot⁡(x))+12(cot⁡2(x)+1)cot⁡(x)coth⁡2(cot⁡(x))csch⁡2(cot⁡(x))csch⁡2(cot⁡(x))+1+4cot⁡2(x)coth⁡(cot⁡(x)))csch⁡(cot⁡(x))csch⁡2(cot⁡(x))+1\frac{\left(\cot^{2}{\left(x \right)} + 1\right) \left(\left(\cot^{2}{\left(x \right)} + 1\right)^{2} \coth^{3}{\left(\cot{\left(x \right)} \right)} + \frac{3 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \coth{\left(\cot{\left(x \right)} \right)}}{\sinh^{2}{\left(\cot{\left(x \right)} \right)}} + \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \cosh{\left(\cot{\left(x \right)} \right)}}{\sinh^{3}{\left(\cot{\left(x \right)} \right)}} - \frac{8 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \coth^{3}{\left(\cot{\left(x \right)} \right)} \operatorname{csch}^{2}{\left(\cot{\left(x \right)} \right)}}{\operatorname{csch}^{2}{\left(\cot{\left(x \right)} \right)} + 1} - \frac{6 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \coth{\left(\cot{\left(x \right)} \right)} \operatorname{csch}^{2}{\left(\cot{\left(x \right)} \right)}}{\left(\operatorname{csch}^{2}{\left(\cot{\left(x \right)} \right)} + 1\right) \sinh^{2}{\left(\cot{\left(x \right)} \right)}} + \frac{8 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \coth^{3}{\left(\cot{\left(x \right)} \right)} \operatorname{csch}^{4}{\left(\cot{\left(x \right)} \right)}}{\left(\operatorname{csch}^{2}{\left(\cot{\left(x \right)} \right)} + 1\right)^{2}} - 6 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} \coth^{2}{\left(\cot{\left(x \right)} \right)} - \frac{6 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}}{\sinh^{2}{\left(\cot{\left(x \right)} \right)}} + 2 \left(\cot^{2}{\left(x \right)} + 1\right) \coth{\left(\cot{\left(x \right)} \right)} + \frac{12 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} \coth^{2}{\left(\cot{\left(x \right)} \right)} \operatorname{csch}^{2}{\left(\cot{\left(x \right)} \right)}}{\operatorname{csch}^{2}{\left(\cot{\left(x \right)} \right)} + 1} + 4 \cot^{2}{\left(x \right)} \coth{\left(\cot{\left(x \right)} \right)}\right) \operatorname{csch}{\left(\cot{\left(x \right)} \right)}}{\operatorname{csch}^{2}{\left(\cot{\left(x \right)} \right)} + 1}
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Gráfico
Derivada de y=arctancsch(cotx)
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