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acos(exp^(2-3x^4))^4÷sqrt(cosh(2x-3))
Derivada de la función/ acos(exp^(2-3x^4))^4÷sqrt(cosh(2x-3))

Derivada de acos(exp^(2-3x^4))^4÷sqrt(cosh(2x-3))

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Gráfico:

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Solución

Ha introducido [src] 
      /        4\
     4| 2 - 3*x |
 acos \E        /
-----------------
  _______________
\/ cosh(2*x - 3)
acos⁡4(e2−3x4)cosh⁡(2x−3)\frac{\operatorname{acos}^{4}{\left(e^{2 - 3 x^{4}} \right)}}{\sqrt{\cosh{\left(2 x - 3 \right)}}} 
acos(E^(2 - 3*x^4))^4/sqrt(cosh(2*x - 3))
Gráfica
02468-8-6-4-2-1010-100100
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
       /        4\                               /        4\         4  
      4| 2 - 3*x |                        3     3| 2 - 3*x |  2 - 3*x   
  acos \E        /*sinh(2*x - 3)      48*x *acos \E        /*e          
- ------------------------------ + -------------------------------------
             3/2                       _______________                  
         cosh   (2*x - 3)             /             4                   
                                     /       4 - 6*x     _______________
                                   \/   1 - e         *\/ cosh(2*x - 3)
48x3e2−3x4acos⁡3(e2−3x4)1−e4−6x4cosh⁡(2x−3)−sinh⁡(2x−3)acos⁡4(e2−3x4)cosh⁡32(2x−3)\frac{48 x^{3} e^{2 - 3 x^{4}} \operatorname{acos}^{3}{\left(e^{2 - 3 x^{4}} \right)}}{\sqrt{1 - e^{4 - 6 x^{4}}} \sqrt{\cosh{\left(2 x - 3 \right)}}} - \frac{\sinh{\left(2 x - 3 \right)} \operatorname{acos}^{4}{\left(e^{2 - 3 x^{4}} \right)}}{\cosh^{\frac{3}{2}}{\left(2 x - 3 \right)}}
Simplificar
Segunda derivada [src] 
                 /                                                   /      /        4\         4                 4            /        4\         4            /        4\         4\             /        4\         4               \
     /        4\ |     /        4\ /           2          \          |      | 2 - 3*x |  2 - 3*x        4  4 - 6*x       4     | 2 - 3*x |  6 - 9*x       4     | 2 - 3*x |  2 - 3*x |       3     | 2 - 3*x |  2 - 3*x                |
    2| 2 - 3*x | |    2| 2 - 3*x | |     3*sinh (-3 + 2*x)|        2 |  acos\e        /*e           12*x *e           4*x *acos\e        /*e           4*x *acos\e        /*e        |   96*x *acos\e        /*e        *sinh(-3 + 2*x)|
acos \e        /*|acos \e        /*|-2 + -----------------| - 144*x *|- ------------------------- - --------------- + ------------------------------ + ------------------------------| - ----------------------------------------------|
                 |                 |          2           |          |         _______________                   4                         3/2                  _______________      |             _______________                     |
                 |                 \      cosh (-3 + 2*x) /          |        /             4             4 - 6*x           /            4\                    /             4       |            /             4                      |
                 |                                                   |       /       4 - 6*x         1 - e                  |     4 - 6*x |                   /       4 - 6*x        |           /       4 - 6*x                       |
                 \                                                   \     \/   1 - e                                       \1 - e        /                 \/   1 - e               /         \/   1 - e         *cosh(-3 + 2*x)      /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                             ________________                                                                                                           
                                                                                                           \/ cosh(-3 + 2*x)
(−96x3e2−3x4sinh⁡(2x−3)acos⁡(e2−3x4)1−e4−6x4cosh⁡(2x−3)−144x2(−12x4e4−6x41−e4−6x4+4x4e2−3x4acos⁡(e2−3x4)1−e4−6x4+4x4e6−9x4acos⁡(e2−3x4)(1−e4−6x4)32−e2−3x4acos⁡(e2−3x4)1−e4−6x4)+(3sinh⁡2(2x−3)cosh⁡2(2x−3)−2)acos⁡2(e2−3x4))acos⁡2(e2−3x4)cosh⁡(2x−3)\frac{\left(- \frac{96 x^{3} e^{2 - 3 x^{4}} \sinh{\left(2 x - 3 \right)} \operatorname{acos}{\left(e^{2 - 3 x^{4}} \right)}}{\sqrt{1 - e^{4 - 6 x^{4}}} \cosh{\left(2 x - 3 \right)}} - 144 x^{2} \left(- \frac{12 x^{4} e^{4 - 6 x^{4}}}{1 - e^{4 - 6 x^{4}}} + \frac{4 x^{4} e^{2 - 3 x^{4}} \operatorname{acos}{\left(e^{2 - 3 x^{4}} \right)}}{\sqrt{1 - e^{4 - 6 x^{4}}}} + \frac{4 x^{4} e^{6 - 9 x^{4}} \operatorname{acos}{\left(e^{2 - 3 x^{4}} \right)}}{\left(1 - e^{4 - 6 x^{4}}\right)^{\frac{3}{2}}} - \frac{e^{2 - 3 x^{4}} \operatorname{acos}{\left(e^{2 - 3 x^{4}} \right)}}{\sqrt{1 - e^{4 - 6 x^{4}}}}\right) + \left(\frac{3 \sinh^{2}{\left(2 x - 3 \right)}}{\cosh^{2}{\left(2 x - 3 \right)}} - 2\right) \operatorname{acos}^{2}{\left(e^{2 - 3 x^{4}} \right)}\right) \operatorname{acos}^{2}{\left(e^{2 - 3 x^{4}} \right)}}{\sqrt{\cosh{\left(2 x - 3 \right)}}}
Simplificar
Tercera derivada [src] 
/                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     /      /        4\         4                 4            /        4\         4            /        4\         4\                               \                
|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     |      | 2 - 3*x |  2 - 3*x        4  4 - 6*x       4     | 2 - 3*x |  6 - 9*x       4     | 2 - 3*x |  2 - 3*x |     /        4\               |                
|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   2 |  acos\e        /*e           12*x *e           4*x *acos\e        /*e           4*x *acos\e        /*e        |     | 2 - 3*x |               |                
|                                                                                                                                                                                                                                                                                                                                                         /        4\ /             2          \                              /        4\ /           2          \         4   432*x *|- ------------------------- - --------------- + ------------------------------ + ------------------------------|*acos\e        /*sinh(-3 + 2*x)|                
|                                                                                                                                                                                                                                                                                                                                                        3| 2 - 3*x | |      15*sinh (-3 + 2*x)|                       3     2| 2 - 3*x | |     3*sinh (-3 + 2*x)|  2 - 3*x           |         _______________                   4                         3/2                  _______________      |                               |                
|      /     /        4\         4                   4               /        4\         4              /        4\          4              /        4\         4              /        4\         4              /        4\         4             /        4\         4              /        4\           4              /        4\         4\   acos \e        /*|-14 + ------------------|*sinh(-3 + 2*x)   144*x *acos \e        /*|-2 + -----------------|*e                  |        /             4             4 - 6*x           /            4\                    /             4       |                               |                
|      |    2| 2 - 3*x |  2 - 3*x          8  6 - 9*x          8     | 2 - 3*x |  4 - 6*x         8     | 2 - 3*x |  8 - 12*x        4     2| 2 - 3*x |  6 - 9*x        4     2| 2 - 3*x |  2 - 3*x        8     2| 2 - 3*x |  2 - 3*x        4     | 2 - 3*x |  4 - 6*x        8     2| 2 - 3*x |  10 - 15*x        8     2| 2 - 3*x |  6 - 9*x |                    |           2            |                                          |          2           |                    |       /       4 - 6*x         1 - e                  |     4 - 6*x |                   /       4 - 6*x        |                               |     /        4\
|      |acos \e        /*e            144*x *e            216*x *acos\e        /*e           216*x *acos\e        /*e            18*x *acos \e        /*e           18*x *acos \e        /*e           24*x *acos \e        /*e           54*x *acos\e        /*e           72*x *acos \e        /*e             96*x *acos \e        /*e        |                    \       cosh (-3 + 2*x)  /                                          \      cosh (-3 + 2*x) /                    \     \/   1 - e                                       \1 - e        /                 \/   1 - e               /                               |     | 2 - 3*x |
|288*x*|-------------------------- + ------------------ - -------------------------------- - --------------------------------- - -------------------------------- - -------------------------------- + -------------------------------- + ------------------------------- + ---------------------------------- + --------------------------------| - ---------------------------------------------------------- + ---------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------|*acos\e        /
|      |       _______________                      3/2                        4                                     2                                 3/2                    _______________                    _______________                               4                                   5/2                                 3/2       |                         cosh(-3 + 2*x)                                                _______________                                                                                            cosh(-3 + 2*x)                                                                    |                
|      |      /             4        /            4\                    4 - 6*x                       /            4\                   /            4\                      /             4                    /             4                         4 - 6*x                     /            4\                     /            4\          |                                                                                      /             4                                                                                                                                                                               |                
|      |     /       4 - 6*x         |     4 - 6*x |               1 - e                              |     4 - 6*x |                   |     4 - 6*x |                     /       4 - 6*x                    /       4 - 6*x                     1 - e                            |     4 - 6*x |                     |     4 - 6*x |          |                                                                                     /       4 - 6*x                                                                                                                                                                                |                
\      \   \/   1 - e                \1 - e        /                                                  \1 - e        /                   \1 - e        /                   \/   1 - e                         \/   1 - e                                                             \1 - e        /                     \1 - e        /          /                                                                                   \/   1 - e                                                                                                                                                                                       /                
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                                                                                                                                                                                                                                                                                                                     ________________                                                                                                                                                                                                                                                                                                                  
                                                                                                                                                                                                                                                                                                                   \/ cosh(-3 + 2*x)
(144x3(3sinh⁡2(2x−3)cosh⁡2(2x−3)−2)e2−3x4acos⁡2(e2−3x4)1−e4−6x4+432x2(−12x4e4−6x41−e4−6x4+4x4e2−3x4acos⁡(e2−3x4)1−e4−6x4+4x4e6−9x4acos⁡(e2−3x4)(1−e4−6x4)32−e2−3x4acos⁡(e2−3x4)1−e4−6x4)sinh⁡(2x−3)acos⁡(e2−3x4)cosh⁡(2x−3)+288x(−216x8e4−6x4acos⁡(e2−3x4)1−e4−6x4−216x8e8−12x4acos⁡(e2−3x4)(1−e4−6x4)2+24x8e2−3x4acos⁡2(e2−3x4)1−e4−6x4+96x8e6−9x4acos⁡2(e2−3x4)(1−e4−6x4)32+144x8e6−9x4(1−e4−6x4)32+72x8e10−15x4acos⁡2(e2−3x4)(1−e4−6x4)52+54x4e4−6x4acos⁡(e2−3x4)1−e4−6x4−18x4e2−3x4acos⁡2(e2−3x4)1−e4−6x4−18x4e6−9x4acos⁡2(e2−3x4)(1−e4−6x4)32+e2−3x4acos⁡2(e2−3x4)1−e4−6x4)−(15sinh⁡2(2x−3)cosh⁡2(2x−3)−14)sinh⁡(2x−3)acos⁡3(e2−3x4)cosh⁡(2x−3))acos⁡(e2−3x4)cosh⁡(2x−3)\frac{\left(\frac{144 x^{3} \left(\frac{3 \sinh^{2}{\left(2 x - 3 \right)}}{\cosh^{2}{\left(2 x - 3 \right)}} - 2\right) e^{2 - 3 x^{4}} \operatorname{acos}^{2}{\left(e^{2 - 3 x^{4}} \right)}}{\sqrt{1 - e^{4 - 6 x^{4}}}} + \frac{432 x^{2} \left(- \frac{12 x^{4} e^{4 - 6 x^{4}}}{1 - e^{4 - 6 x^{4}}} + \frac{4 x^{4} e^{2 - 3 x^{4}} \operatorname{acos}{\left(e^{2 - 3 x^{4}} \right)}}{\sqrt{1 - e^{4 - 6 x^{4}}}} + \frac{4 x^{4} e^{6 - 9 x^{4}} \operatorname{acos}{\left(e^{2 - 3 x^{4}} \right)}}{\left(1 - e^{4 - 6 x^{4}}\right)^{\frac{3}{2}}} - \frac{e^{2 - 3 x^{4}} \operatorname{acos}{\left(e^{2 - 3 x^{4}} \right)}}{\sqrt{1 - e^{4 - 6 x^{4}}}}\right) \sinh{\left(2 x - 3 \right)} \operatorname{acos}{\left(e^{2 - 3 x^{4}} \right)}}{\cosh{\left(2 x - 3 \right)}} + 288 x \left(- \frac{216 x^{8} e^{4 - 6 x^{4}} \operatorname{acos}{\left(e^{2 - 3 x^{4}} \right)}}{1 - e^{4 - 6 x^{4}}} - \frac{216 x^{8} e^{8 - 12 x^{4}} \operatorname{acos}{\left(e^{2 - 3 x^{4}} \right)}}{\left(1 - e^{4 - 6 x^{4}}\right)^{2}} + \frac{24 x^{8} e^{2 - 3 x^{4}} \operatorname{acos}^{2}{\left(e^{2 - 3 x^{4}} \right)}}{\sqrt{1 - e^{4 - 6 x^{4}}}} + \frac{96 x^{8} e^{6 - 9 x^{4}} \operatorname{acos}^{2}{\left(e^{2 - 3 x^{4}} \right)}}{\left(1 - e^{4 - 6 x^{4}}\right)^{\frac{3}{2}}} + \frac{144 x^{8} e^{6 - 9 x^{4}}}{\left(1 - e^{4 - 6 x^{4}}\right)^{\frac{3}{2}}} + \frac{72 x^{8} e^{10 - 15 x^{4}} \operatorname{acos}^{2}{\left(e^{2 - 3 x^{4}} \right)}}{\left(1 - e^{4 - 6 x^{4}}\right)^{\frac{5}{2}}} + \frac{54 x^{4} e^{4 - 6 x^{4}} \operatorname{acos}{\left(e^{2 - 3 x^{4}} \right)}}{1 - e^{4 - 6 x^{4}}} - \frac{18 x^{4} e^{2 - 3 x^{4}} \operatorname{acos}^{2}{\left(e^{2 - 3 x^{4}} \right)}}{\sqrt{1 - e^{4 - 6 x^{4}}}} - \frac{18 x^{4} e^{6 - 9 x^{4}} \operatorname{acos}^{2}{\left(e^{2 - 3 x^{4}} \right)}}{\left(1 - e^{4 - 6 x^{4}}\right)^{\frac{3}{2}}} + \frac{e^{2 - 3 x^{4}} \operatorname{acos}^{2}{\left(e^{2 - 3 x^{4}} \right)}}{\sqrt{1 - e^{4 - 6 x^{4}}}}\right) - \frac{\left(\frac{15 \sinh^{2}{\left(2 x - 3 \right)}}{\cosh^{2}{\left(2 x - 3 \right)}} - 14\right) \sinh{\left(2 x - 3 \right)} \operatorname{acos}^{3}{\left(e^{2 - 3 x^{4}} \right)}}{\cosh{\left(2 x - 3 \right)}}\right) \operatorname{acos}{\left(e^{2 - 3 x^{4}} \right)}}{\sqrt{\cosh{\left(2 x - 3 \right)}}}
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Gráfico
Derivada de acos(exp^(2-3x^4))^4÷sqrt(cosh(2x-3))
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