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Derivada de la función/ coshx/ y=tan/ y=tan^-3(e^coshx)^1÷2

Derivada de y=tan^-3(e^coshx)^1÷2

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

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Definida a trozos:

Solución

Ha introducido [src] 
                 ____
               \/ -3 
/   / cosh(x)\\      
\tan\E       //
tan⁡−3(ecosh⁡(x))\tan^{\sqrt{-3}}{\left(e^{\cosh{\left(x \right)}} \right)} 
tan(E^cosh(x))^(sqrt(-3))
Primera derivada [src] 
                         ____                                      
                       \/ -3                                       
    ___ /   / cosh(x)\\       /       2/ cosh(x)\\  cosh(x)        
I*\/ 3 *\tan\E       //      *\1 + tan \E       //*e       *sinh(x)
-------------------------------------------------------------------
                              / cosh(x)\                           
                           tan\E       /
3i(tan⁡2(ecosh⁡(x))+1)ecosh⁡(x)tan⁡−3(ecosh⁡(x))sinh⁡(x)tan⁡(ecosh⁡(x))\frac{\sqrt{3} i \left(\tan^{2}{\left(e^{\cosh{\left(x \right)}} \right)} + 1\right) e^{\cosh{\left(x \right)}} \tan^{\sqrt{-3}}{\left(e^{\cosh{\left(x \right)}} \right)} \sinh{\left(x \right)}}{\tan{\left(e^{\cosh{\left(x \right)}} \right)}}
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Segunda derivada [src] 
                   ___                                                                                                                                                                                             
               I*\/ 3                       /    ___     2          ___                 2    /       2/ cosh(x)\\  cosh(x)                                     ___     2    /       2/ cosh(x)\\  cosh(x)\         
/   / cosh(x)\\        /       2/ cosh(x)\\ |I*\/ 3 *sinh (x)   I*\/ 3 *cosh(x)   3*sinh (x)*\1 + tan \E       //*e                ___     2     cosh(x)   I*\/ 3 *sinh (x)*\1 + tan \E       //*e       |  cosh(x)
\tan\E       //       *\1 + tan \E       //*|---------------- + --------------- - ---------------------------------------- + 2*I*\/ 3 *sinh (x)*e        - ----------------------------------------------|*e       
                                            |    / cosh(x)\         / cosh(x)\                    2/ cosh(x)\                                                                 2/ cosh(x)\                |         
                                            \ tan\E       /      tan\E       /                 tan \E       /                                                              tan \E       /                /
(tan⁡2(ecosh⁡(x))+1)(−3(tan⁡2(ecosh⁡(x))+1)ecosh⁡(x)sinh⁡2(x)tan⁡2(ecosh⁡(x))−3i(tan⁡2(ecosh⁡(x))+1)ecosh⁡(x)sinh⁡2(x)tan⁡2(ecosh⁡(x))+23iecosh⁡(x)sinh⁡2(x)+3isinh⁡2(x)tan⁡(ecosh⁡(x))+3icosh⁡(x)tan⁡(ecosh⁡(x)))ecosh⁡(x)tan⁡3i(ecosh⁡(x))\left(\tan^{2}{\left(e^{\cosh{\left(x \right)}} \right)} + 1\right) \left(- \frac{3 \left(\tan^{2}{\left(e^{\cosh{\left(x \right)}} \right)} + 1\right) e^{\cosh{\left(x \right)}} \sinh^{2}{\left(x \right)}}{\tan^{2}{\left(e^{\cosh{\left(x \right)}} \right)}} - \frac{\sqrt{3} i \left(\tan^{2}{\left(e^{\cosh{\left(x \right)}} \right)} + 1\right) e^{\cosh{\left(x \right)}} \sinh^{2}{\left(x \right)}}{\tan^{2}{\left(e^{\cosh{\left(x \right)}} \right)}} + 2 \sqrt{3} i e^{\cosh{\left(x \right)}} \sinh^{2}{\left(x \right)} + \frac{\sqrt{3} i \sinh^{2}{\left(x \right)}}{\tan{\left(e^{\cosh{\left(x \right)}} \right)}} + \frac{\sqrt{3} i \cosh{\left(x \right)}}{\tan{\left(e^{\cosh{\left(x \right)}} \right)}}\right) e^{\cosh{\left(x \right)}} \tan^{\sqrt{3} i}{\left(e^{\cosh{\left(x \right)}} \right)}
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Tercera derivada [src] 
                   ___                      /                                                                                                                                                                                                                                                                           2                                                                                                 2                                                                                                                                                                              \                 
               I*\/ 3                       |       ___          ___     2             2    /       2/ cosh(x)\\  2*cosh(x)         2    /       2/ cosh(x)\\  cosh(x)     /       2/ cosh(x)\\          cosh(x)         ___                                                                        /       2/ cosh(x)\\      2     2*cosh(x)                                                     ___ /       2/ cosh(x)\\      2     2*cosh(x)         ___     2    /       2/ cosh(x)\\  2*cosh(x)         ___     2    /       2/ cosh(x)\\  cosh(x)         ___ /       2/ cosh(x)\\          cosh(x)|                 
/   / cosh(x)\\        /       2/ cosh(x)\\ |   I*\/ 3       I*\/ 3 *sinh (x)   18*sinh (x)*\1 + tan \E       //*e            9*sinh (x)*\1 + tan \E       //*e          9*\1 + tan \E       //*cosh(x)*e          3*I*\/ 3 *cosh(x)         ___     2     cosh(x)         ___          cosh(x)   9*\1 + tan \E       // *sinh (x)*e                  ___     2     2*cosh(x)    / cosh(x)\   I*\/ 3 *\1 + tan \E       // *sinh (x)*e            4*I*\/ 3 *sinh (x)*\1 + tan \E       //*e            3*I*\/ 3 *sinh (x)*\1 + tan \E       //*e          3*I*\/ 3 *\1 + tan \E       //*cosh(x)*e       |  cosh(x)        
\tan\E       //       *\1 + tan \E       //*|------------- + ---------------- - ------------------------------------------- - ---------------------------------------- - --------------------------------------- + ----------------- + 6*I*\/ 3 *sinh (x)*e        + 6*I*\/ 3 *cosh(x)*e        + ------------------------------------------- + 4*I*\/ 3 *sinh (x)*e         *tan\E       / - ------------------------------------------------- - -------------------------------------------------- - ------------------------------------------------ - -----------------------------------------------|*e       *sinh(x)
                                            |   / cosh(x)\       / cosh(x)\                       / cosh(x)\                                  2/ cosh(x)\                                2/ cosh(x)\                    / cosh(x)\                                                                                  3/ cosh(x)\                                                                                    3/ cosh(x)\                                         / cosh(x)\                                          2/ cosh(x)\                                        2/ cosh(x)\                |                 
                                            \tan\E       /    tan\E       /                    tan\E       /                               tan \E       /                             tan \E       /                 tan\E       /                                                                               tan \E       /                                                                                 tan \E       /                                      tan\E       /                                       tan \E       /                                     tan \E       /                /
(tan⁡2(ecosh⁡(x))+1)(9(tan⁡2(ecosh⁡(x))+1)2e2cosh⁡(x)sinh⁡2(x)tan⁡3(ecosh⁡(x))−3i(tan⁡2(ecosh⁡(x))+1)2e2cosh⁡(x)sinh⁡2(x)tan⁡3(ecosh⁡(x))−18(tan⁡2(ecosh⁡(x))+1)e2cosh⁡(x)sinh⁡2(x)tan⁡(ecosh⁡(x))−43i(tan⁡2(ecosh⁡(x))+1)e2cosh⁡(x)sinh⁡2(x)tan⁡(ecosh⁡(x))−9(tan⁡2(ecosh⁡(x))+1)ecosh⁡(x)sinh⁡2(x)tan⁡2(ecosh⁡(x))−33i(tan⁡2(ecosh⁡(x))+1)ecosh⁡(x)sinh⁡2(x)tan⁡2(ecosh⁡(x))−9(tan⁡2(ecosh⁡(x))+1)ecosh⁡(x)cosh⁡(x)tan⁡2(ecosh⁡(x))−33i(tan⁡2(ecosh⁡(x))+1)ecosh⁡(x)cosh⁡(x)tan⁡2(ecosh⁡(x))+43ie2cosh⁡(x)tan⁡(ecosh⁡(x))sinh⁡2(x)+63iecosh⁡(x)sinh⁡2(x)+63iecosh⁡(x)cosh⁡(x)+3isinh⁡2(x)tan⁡(ecosh⁡(x))+33icosh⁡(x)tan⁡(ecosh⁡(x))+3itan⁡(ecosh⁡(x)))ecosh⁡(x)tan⁡3i(ecosh⁡(x))sinh⁡(x)\left(\tan^{2}{\left(e^{\cosh{\left(x \right)}} \right)} + 1\right) \left(\frac{9 \left(\tan^{2}{\left(e^{\cosh{\left(x \right)}} \right)} + 1\right)^{2} e^{2 \cosh{\left(x \right)}} \sinh^{2}{\left(x \right)}}{\tan^{3}{\left(e^{\cosh{\left(x \right)}} \right)}} - \frac{\sqrt{3} i \left(\tan^{2}{\left(e^{\cosh{\left(x \right)}} \right)} + 1\right)^{2} e^{2 \cosh{\left(x \right)}} \sinh^{2}{\left(x \right)}}{\tan^{3}{\left(e^{\cosh{\left(x \right)}} \right)}} - \frac{18 \left(\tan^{2}{\left(e^{\cosh{\left(x \right)}} \right)} + 1\right) e^{2 \cosh{\left(x \right)}} \sinh^{2}{\left(x \right)}}{\tan{\left(e^{\cosh{\left(x \right)}} \right)}} - \frac{4 \sqrt{3} i \left(\tan^{2}{\left(e^{\cosh{\left(x \right)}} \right)} + 1\right) e^{2 \cosh{\left(x \right)}} \sinh^{2}{\left(x \right)}}{\tan{\left(e^{\cosh{\left(x \right)}} \right)}} - \frac{9 \left(\tan^{2}{\left(e^{\cosh{\left(x \right)}} \right)} + 1\right) e^{\cosh{\left(x \right)}} \sinh^{2}{\left(x \right)}}{\tan^{2}{\left(e^{\cosh{\left(x \right)}} \right)}} - \frac{3 \sqrt{3} i \left(\tan^{2}{\left(e^{\cosh{\left(x \right)}} \right)} + 1\right) e^{\cosh{\left(x \right)}} \sinh^{2}{\left(x \right)}}{\tan^{2}{\left(e^{\cosh{\left(x \right)}} \right)}} - \frac{9 \left(\tan^{2}{\left(e^{\cosh{\left(x \right)}} \right)} + 1\right) e^{\cosh{\left(x \right)}} \cosh{\left(x \right)}}{\tan^{2}{\left(e^{\cosh{\left(x \right)}} \right)}} - \frac{3 \sqrt{3} i \left(\tan^{2}{\left(e^{\cosh{\left(x \right)}} \right)} + 1\right) e^{\cosh{\left(x \right)}} \cosh{\left(x \right)}}{\tan^{2}{\left(e^{\cosh{\left(x \right)}} \right)}} + 4 \sqrt{3} i e^{2 \cosh{\left(x \right)}} \tan{\left(e^{\cosh{\left(x \right)}} \right)} \sinh^{2}{\left(x \right)} + 6 \sqrt{3} i e^{\cosh{\left(x \right)}} \sinh^{2}{\left(x \right)} + 6 \sqrt{3} i e^{\cosh{\left(x \right)}} \cosh{\left(x \right)} + \frac{\sqrt{3} i \sinh^{2}{\left(x \right)}}{\tan{\left(e^{\cosh{\left(x \right)}} \right)}} + \frac{3 \sqrt{3} i \cosh{\left(x \right)}}{\tan{\left(e^{\cosh{\left(x \right)}} \right)}} + \frac{\sqrt{3} i}{\tan{\left(e^{\cosh{\left(x \right)}} \right)}}\right) e^{\cosh{\left(x \right)}} \tan^{\sqrt{3} i}{\left(e^{\cosh{\left(x \right)}} \right)} \sinh{\left(x \right)}
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