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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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Solución

Ha introducido [src] 
       1        
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   3/ cosh(x)\  
tan \E       /*2
12tan⁡3(ecosh⁡(x))\frac{1}{2 \tan^{3}{\left(e^{\cosh{\left(x \right)}} \right)}} 
1/(tan(E^cosh(x))^3*2)
Primera derivada [src] 
   /       2/ cosh(x)\\  cosh(x)        
-3*\1 + tan \E       //*e       *sinh(x)
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                 4/ cosh(x)\            
            2*tan \E       /
−3(tan⁡2(ecosh⁡(x))+1)ecosh⁡(x)sinh⁡(x)2tan⁡4(ecosh⁡(x))- \frac{3 \left(\tan^{2}{\left(e^{\cosh{\left(x \right)}} \right)} + 1\right) e^{\cosh{\left(x \right)}} \sinh{\left(x \right)}}{2 \tan^{4}{\left(e^{\cosh{\left(x \right)}} \right)}}
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Segunda derivada [src] 
                        /       2                                                    2    /       2/ cosh(x)\\  cosh(x)\         
   /       2/ cosh(x)\\ |   sinh (x)        cosh(x)            2     cosh(x)   4*sinh (x)*\1 + tan \E       //*e       |  cosh(x)
-3*\1 + tan \E       //*|------------- + ------------- + 2*sinh (x)*e        - ----------------------------------------|*e       
                        |   / cosh(x)\      / cosh(x)\                                         2/ cosh(x)\             |         
                        \tan\E       /   tan\E       /                                      tan \E       /             /         
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                                                              3/ cosh(x)\                                                        
                                                         2*tan \E       /
−3(tan⁡2(ecosh⁡(x))+1)(−4(tan⁡2(ecosh⁡(x))+1)ecosh⁡(x)sinh⁡2(x)tan⁡2(ecosh⁡(x))+2ecosh⁡(x)sinh⁡2(x)+sinh⁡2(x)tan⁡(ecosh⁡(x))+cosh⁡(x)tan⁡(ecosh⁡(x)))ecosh⁡(x)2tan⁡3(ecosh⁡(x))- \frac{3 \left(\tan^{2}{\left(e^{\cosh{\left(x \right)}} \right)} + 1\right) \left(- \frac{4 \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 e^{\cosh{\left(x \right)}} \sinh^{2}{\left(x \right)} + \frac{\sinh^{2}{\left(x \right)}}{\tan{\left(e^{\cosh{\left(x \right)}} \right)}} + \frac{\cosh{\left(x \right)}}{\tan{\left(e^{\cosh{\left(x \right)}} \right)}}\right) e^{\cosh{\left(x \right)}}}{2 \tan^{3}{\left(e^{\cosh{\left(x \right)}} \right)}}
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Tercera derivada [src] 
                        /                                                                                                                                                                                                                                                                                  2                    \                 
                        |                        2                                                        2     cosh(x)              cosh(x)          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)\\ |      1             sinh (x)        3*cosh(x)            2     2*cosh(x)   6*sinh (x)*e          6*cosh(x)*e          22*sinh (x)*\1 + tan \E       //*e            12*sinh (x)*\1 + tan \E       //*e          12*\1 + tan \E       //*cosh(x)*e          20*\1 + tan \E       // *sinh (x)*e         |  cosh(x)        
-3*\1 + tan \E       //*|-------------- + -------------- + -------------- + 4*sinh (x)*e          + ------------------- + ------------------ - ------------------------------------------- - ----------------------------------------- - ---------------------------------------- + --------------------------------------------|*e       *sinh(x)
                        |   2/ cosh(x)\      2/ cosh(x)\      2/ cosh(x)\                                 / cosh(x)\           / cosh(x)\                        2/ cosh(x)\                                  3/ cosh(x)\                                3/ cosh(x)\                                  4/ cosh(x)\               |                 
                        \tan \E       /   tan \E       /   tan \E       /                              tan\E       /        tan\E       /                     tan \E       /                               tan \E       /                             tan \E       /                               tan \E       /               /                 
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                                                                                                                                                                      2/ cosh(x)\                                                                                                                                                                 
                                                                                                                                                                 2*tan \E       /
−3(tan⁡2(ecosh⁡(x))+1)(20(tan⁡2(ecosh⁡(x))+1)2e2cosh⁡(x)sinh⁡2(x)tan⁡4(ecosh⁡(x))−22(tan⁡2(ecosh⁡(x))+1)e2cosh⁡(x)sinh⁡2(x)tan⁡2(ecosh⁡(x))−12(tan⁡2(ecosh⁡(x))+1)ecosh⁡(x)sinh⁡2(x)tan⁡3(ecosh⁡(x))−12(tan⁡2(ecosh⁡(x))+1)ecosh⁡(x)cosh⁡(x)tan⁡3(ecosh⁡(x))+4e2cosh⁡(x)sinh⁡2(x)+6ecosh⁡(x)sinh⁡2(x)tan⁡(ecosh⁡(x))+6ecosh⁡(x)cosh⁡(x)tan⁡(ecosh⁡(x))+sinh⁡2(x)tan⁡2(ecosh⁡(x))+3cosh⁡(x)tan⁡2(ecosh⁡(x))+1tan⁡2(ecosh⁡(x)))ecosh⁡(x)sinh⁡(x)2tan⁡2(ecosh⁡(x))- \frac{3 \left(\tan^{2}{\left(e^{\cosh{\left(x \right)}} \right)} + 1\right) \left(\frac{20 \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^{4}{\left(e^{\cosh{\left(x \right)}} \right)}} - \frac{22 \left(\tan^{2}{\left(e^{\cosh{\left(x \right)}} \right)} + 1\right) e^{2 \cosh{\left(x \right)}} \sinh^{2}{\left(x \right)}}{\tan^{2}{\left(e^{\cosh{\left(x \right)}} \right)}} - \frac{12 \left(\tan^{2}{\left(e^{\cosh{\left(x \right)}} \right)} + 1\right) e^{\cosh{\left(x \right)}} \sinh^{2}{\left(x \right)}}{\tan^{3}{\left(e^{\cosh{\left(x \right)}} \right)}} - \frac{12 \left(\tan^{2}{\left(e^{\cosh{\left(x \right)}} \right)} + 1\right) e^{\cosh{\left(x \right)}} \cosh{\left(x \right)}}{\tan^{3}{\left(e^{\cosh{\left(x \right)}} \right)}} + 4 e^{2 \cosh{\left(x \right)}} \sinh^{2}{\left(x \right)} + \frac{6 e^{\cosh{\left(x \right)}} \sinh^{2}{\left(x \right)}}{\tan{\left(e^{\cosh{\left(x \right)}} \right)}} + \frac{6 e^{\cosh{\left(x \right)}} \cosh{\left(x \right)}}{\tan{\left(e^{\cosh{\left(x \right)}} \right)}} + \frac{\sinh^{2}{\left(x \right)}}{\tan^{2}{\left(e^{\cosh{\left(x \right)}} \right)}} + \frac{3 \cosh{\left(x \right)}}{\tan^{2}{\left(e^{\cosh{\left(x \right)}} \right)}} + \frac{1}{\tan^{2}{\left(e^{\cosh{\left(x \right)}} \right)}}\right) e^{\cosh{\left(x \right)}} \sinh{\left(x \right)}}{2 \tan^{2}{\left(e^{\cosh{\left(x \right)}} \right)}}
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