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coth^-1(secx)
Derivada de la función/ coth^-1(secx)

Derivada de coth^-1(secx)

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src] 
     1      
------------
coth(sec(x))
1coth⁡(sec⁡(x))\frac{1}{\coth{\left(\sec{\left(x \right)} \right)}} 
1/coth(sec(x))
Gráfica
02468-8-6-4-2-10102-2
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
       sec(x)*tan(x)       
---------------------------
    2             2        
coth (sec(x))*sinh (sec(x))
tan⁡(x)sec⁡(x)sinh⁡2(sec⁡(x))coth⁡2(sec⁡(x))\frac{\tan{\left(x \right)} \sec{\left(x \right)}}{\sinh^{2}{\left(\sec{\left(x \right)} \right)} \coth^{2}{\left(\sec{\left(x \right)} \right)}}
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Segunda derivada [src] 
/                     2                                    2               \       
|         2      2*tan (x)*cosh(sec(x))*sec(x)        2*tan (x)*sec(x)     |       
|1 + 2*tan (x) - ----------------------------- + --------------------------|*sec(x)
|                         sinh(sec(x))                            2        |       
\                                                coth(sec(x))*sinh (sec(x))/       
-----------------------------------------------------------------------------------
                                2             2                                    
                            coth (sec(x))*sinh (sec(x))
(2tan⁡2(x)−2tan⁡2(x)cosh⁡(sec⁡(x))sec⁡(x)sinh⁡(sec⁡(x))+2tan⁡2(x)sec⁡(x)sinh⁡2(sec⁡(x))coth⁡(sec⁡(x))+1)sec⁡(x)sinh⁡2(sec⁡(x))coth⁡2(sec⁡(x))\frac{\left(2 \tan^{2}{\left(x \right)} - \frac{2 \tan^{2}{\left(x \right)} \cosh{\left(\sec{\left(x \right)} \right)} \sec{\left(x \right)}}{\sinh{\left(\sec{\left(x \right)} \right)}} + \frac{2 \tan^{2}{\left(x \right)} \sec{\left(x \right)}}{\sinh^{2}{\left(\sec{\left(x \right)} \right)} \coth{\left(\sec{\left(x \right)} \right)}} + 1\right) \sec{\left(x \right)}}{\sinh^{2}{\left(\sec{\left(x \right)} \right)} \coth^{2}{\left(\sec{\left(x \right)} \right)}}
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Tercera derivada [src] 
/                                         2                            /       2   \                             2            2       2                2                      /       2   \                      2       2                 2       2                \              
|         2           2       2      6*tan (x)*cosh(sec(x))*sec(x)   6*\1 + tan (x)/*cosh(sec(x))*sec(x)   6*cosh (sec(x))*sec (x)*tan (x)        6*tan (x)*sec(x)          6*\1 + tan (x)/*sec(x)          6*sec (x)*tan (x)        12*sec (x)*tan (x)*cosh(sec(x))|              
|5 + 6*tan (x) - 2*sec (x)*tan (x) - ----------------------------- - ----------------------------------- + ------------------------------- + -------------------------- + -------------------------- + --------------------------- - -------------------------------|*sec(x)*tan(x)
|                                             sinh(sec(x))                       sinh(sec(x))                           2                                     2                            2               2             4                               3          |              
\                                                                                                                   sinh (sec(x))            coth(sec(x))*sinh (sec(x))   coth(sec(x))*sinh (sec(x))   coth (sec(x))*sinh (sec(x))      coth(sec(x))*sinh (sec(x))  /              
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                                                                                                                                2             2                                                                                                                                    
                                                                                                                            coth (sec(x))*sinh (sec(x))
(−6(tan⁡2(x)+1)cosh⁡(sec⁡(x))sec⁡(x)sinh⁡(sec⁡(x))+6(tan⁡2(x)+1)sec⁡(x)sinh⁡2(sec⁡(x))coth⁡(sec⁡(x))−2tan⁡2(x)sec⁡2(x)+6tan⁡2(x)−6tan⁡2(x)cosh⁡(sec⁡(x))sec⁡(x)sinh⁡(sec⁡(x))+6tan⁡2(x)cosh⁡2(sec⁡(x))sec⁡2(x)sinh⁡2(sec⁡(x))+6tan⁡2(x)sec⁡(x)sinh⁡2(sec⁡(x))coth⁡(sec⁡(x))−12tan⁡2(x)cosh⁡(sec⁡(x))sec⁡2(x)sinh⁡3(sec⁡(x))coth⁡(sec⁡(x))+6tan⁡2(x)sec⁡2(x)sinh⁡4(sec⁡(x))coth⁡2(sec⁡(x))+5)tan⁡(x)sec⁡(x)sinh⁡2(sec⁡(x))coth⁡2(sec⁡(x))\frac{\left(- \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \cosh{\left(\sec{\left(x \right)} \right)} \sec{\left(x \right)}}{\sinh{\left(\sec{\left(x \right)} \right)}} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \sec{\left(x \right)}}{\sinh^{2}{\left(\sec{\left(x \right)} \right)} \coth{\left(\sec{\left(x \right)} \right)}} - 2 \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 6 \tan^{2}{\left(x \right)} - \frac{6 \tan^{2}{\left(x \right)} \cosh{\left(\sec{\left(x \right)} \right)} \sec{\left(x \right)}}{\sinh{\left(\sec{\left(x \right)} \right)}} + \frac{6 \tan^{2}{\left(x \right)} \cosh^{2}{\left(\sec{\left(x \right)} \right)} \sec^{2}{\left(x \right)}}{\sinh^{2}{\left(\sec{\left(x \right)} \right)}} + \frac{6 \tan^{2}{\left(x \right)} \sec{\left(x \right)}}{\sinh^{2}{\left(\sec{\left(x \right)} \right)} \coth{\left(\sec{\left(x \right)} \right)}} - \frac{12 \tan^{2}{\left(x \right)} \cosh{\left(\sec{\left(x \right)} \right)} \sec^{2}{\left(x \right)}}{\sinh^{3}{\left(\sec{\left(x \right)} \right)} \coth{\left(\sec{\left(x \right)} \right)}} + \frac{6 \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)}}{\sinh^{4}{\left(\sec{\left(x \right)} \right)} \coth^{2}{\left(\sec{\left(x \right)} \right)}} + 5\right) \tan{\left(x \right)} \sec{\left(x \right)}}{\sinh^{2}{\left(\sec{\left(x \right)} \right)} \coth^{2}{\left(\sec{\left(x \right)} \right)}}
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Gráfico
Derivada de coth^-1(secx)
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