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cos(5^x-x)^6+tan(e^4*x/(1-e^4*x))+tan(log(8))
Derivada de la función/ cos(5^x-x)^6+tan(e^4*x/(1-e^4*x))+tan(log(8))

Derivada de cos(5^x-x)^6+tan(e^4*x/(1-e^4*x))+tan(log(8))

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

Gráfico:

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Solución

Ha introducido [src] 
                  /   4    \              
   6/ x    \      |  E *x  |              
cos \5  - x/ + tan|--------| + tan(log(8))
                  |     4  |              
                  \1 - E *x/
(cos⁡6(5x−x)+tan⁡(e4x−e4x+1))+tan⁡(log⁡(8))\left(\cos^{6}{\left(5^{x} - x \right)} + \tan{\left(\frac{e^{4} x}{- e^{4} x + 1} \right)}\right) + \tan{\left(\log{\left(8 \right)} \right)} 
cos(5^x - x)^6 + tan((E^4*x)/(1 - E^4*x)) + tan(log(8))
Gráfica
02468-8-6-4-2-1010-2000000020000000
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Primera derivada [src] 
/        /   4    \\ /    4             8   \                                              
|       2|  E *x  || |   e           x*e    |        5/ x    \ /      x       \    / x    \
|1 + tan |--------||*|-------- + -----------| - 6*cos \5  - x/*\-1 + 5 *log(5)/*sin\5  - x/
|        |     4  || |     4               2|                                              
\        \1 - E *x// |1 - E *x   /     4  \ |                                              
                     \           \1 - E *x/ /
−6(5xlog⁡(5)−1)sin⁡(5x−x)cos⁡5(5x−x)+(xe8(−e4x+1)2+e4−e4x+1)(tan⁡2(e4x−e4x+1)+1)- 6 \left(5^{x} \log{\left(5 \right)} - 1\right) \sin{\left(5^{x} - x \right)} \cos^{5}{\left(5^{x} - x \right)} + \left(\frac{x e^{8}}{\left(- e^{4} x + 1\right)^{2}} + \frac{e^{4}}{- e^{4} x + 1}\right) \left(\tan^{2}{\left(\frac{e^{4} x}{- e^{4} x + 1} \right)} + 1\right)
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Segunda derivada [src] 
  /                                                                                                                                                                                          2                                        \
  |                                                                                      /        /      4  \\ /           4  \                                              /           4  \  /        /      4  \\       /      4  \|
  |                                                                                      |       2|   x*e   || |        x*e   |  8                                           |        x*e   |  |       2|   x*e   ||  8    |   x*e   ||
  |                                                                                      |1 + tan |---------||*|-1 + ---------|*e                                            |-1 + ---------| *|1 + tan |---------||*e *tan|---------||
  |                    2                                   2                             |        |        4|| |             4|                                              |             4|  |        |        4||       |        4||
  |    /      x       \     6/ x    \      /      x       \     4/ x    \    2/ x    \   \        \-1 + x*e // \     -1 + x*e /         x    5/ x    \    2       / x    \   \     -1 + x*e /  \        \-1 + x*e //       \-1 + x*e /|
2*|- 3*\-1 + 5 *log(5)/ *cos \5  - x/ + 15*\-1 + 5 *log(5)/ *cos \5  - x/*sin \5  - x/ - ----------------------------------------- - 3*5 *cos \5  - x/*log (5)*sin\5  - x/ - ---------------------------------------------------------|
  |                                                                                                                2                                                                                           2                      |
  |                                                                                                     /        4\                                                                                 /        4\                       |
  \                                                                                                     \-1 + x*e /                                                                                 \-1 + x*e /                       /
2(−3⋅5xlog⁡(5)2sin⁡(5x−x)cos⁡5(5x−x)+15(5xlog⁡(5)−1)2sin⁡2(5x−x)cos⁡4(5x−x)−3(5xlog⁡(5)−1)2cos⁡6(5x−x)−(xe4xe4−1−1)2(tan⁡2(xe4xe4−1)+1)e8tan⁡(xe4xe4−1)(xe4−1)2−(xe4xe4−1−1)(tan⁡2(xe4xe4−1)+1)e8(xe4−1)2)2 \left(- 3 \cdot 5^{x} \log{\left(5 \right)}^{2} \sin{\left(5^{x} - x \right)} \cos^{5}{\left(5^{x} - x \right)} + 15 \left(5^{x} \log{\left(5 \right)} - 1\right)^{2} \sin^{2}{\left(5^{x} - x \right)} \cos^{4}{\left(5^{x} - x \right)} - 3 \left(5^{x} \log{\left(5 \right)} - 1\right)^{2} \cos^{6}{\left(5^{x} - x \right)} - \frac{\left(\frac{x e^{4}}{x e^{4} - 1} - 1\right)^{2} \left(\tan^{2}{\left(\frac{x e^{4}}{x e^{4} - 1} \right)} + 1\right) e^{8} \tan{\left(\frac{x e^{4}}{x e^{4} - 1} \right)}}{\left(x e^{4} - 1\right)^{2}} - \frac{\left(\frac{x e^{4}}{x e^{4} - 1} - 1\right) \left(\tan^{2}{\left(\frac{x e^{4}}{x e^{4} - 1} \right)} + 1\right) e^{8}}{\left(x e^{4} - 1\right)^{2}}\right)
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Tercera derivada [src] 
  /                                                                                                                        2                 3                                                                                                                                                             3                                                               2                                                                                                    \
  |                                                                                                   /        /      4  \\  /           4  \                                                                                               /        /      4  \\ /           4  \         /           4  \      /      4  \ /        /      4  \\         /           4  \  /        /      4  \\        /      4  \                                                           |
  |                                                                                                   |       2|   x*e   ||  |        x*e   |   12                                                                                          |       2|   x*e   || |        x*e   |  12     |        x*e   |     2|   x*e   | |       2|   x*e   ||  12     |        x*e   |  |       2|   x*e   ||  12    |   x*e   |                                                           |
  |                                                                                                   |1 + tan |---------|| *|-1 + ---------| *e                                                                                          3*|1 + tan |---------||*|-1 + ---------|*e     2*|-1 + ---------| *tan |---------|*|1 + tan |---------||*e     6*|-1 + ---------| *|1 + tan |---------||*e  *tan|---------|                                                           |
  |                     3                                                3                            |        |        4||  |             4|                                                                                               |        |        4|| |             4|         |             4|      |        4| |        |        4||         |             4|  |        |        4||        |        4|                                                           |
  |     /      x       \     3/ x    \    3/ x    \      /      x       \     5/ x    \    / x    \   \        \-1 + x*e //  \     -1 + x*e /           x    6/ x    \    2    /      x       \      x    5/ x    \    3       / x    \     \        \-1 + x*e // \     -1 + x*e /         \     -1 + x*e /      \-1 + x*e / \        \-1 + x*e //         \     -1 + x*e /  \        \-1 + x*e //        \-1 + x*e /       x    4/ x    \    2       2/ x    \ /      x       \|
2*|- 60*\-1 + 5 *log(5)/ *cos \5  - x/*sin \5  - x/ + 48*\-1 + 5 *log(5)/ *cos \5  - x/*sin\5  - x/ + -------------------------------------------- - 9*5 *cos \5  - x/*log (5)*\-1 + 5 *log(5)/ - 3*5 *cos \5  - x/*log (5)*sin\5  - x/ + -------------------------------------------- + ------------------------------------------------------------- + ------------------------------------------------------------ + 45*5 *cos \5  - x/*log (5)*sin \5  - x/*\-1 + 5 *log(5)/|
  |                                                                                                                              3                                                                                                                                   3                                                       3                                                              3                                                                                   |
  |                                                                                                                   /        4\                                                                                                                         /        4\                                             /        4\                                                    /        4\                                                                                    |
  \                                                                                                                   \-1 + x*e /                                                                                                                         \-1 + x*e /                                             \-1 + x*e /                                                    \-1 + x*e /                                                                                    /
2(45⋅5x(5xlog⁡(5)−1)log⁡(5)2sin⁡2(5x−x)cos⁡4(5x−x)−9⋅5x(5xlog⁡(5)−1)log⁡(5)2cos⁡6(5x−x)−3⋅5xlog⁡(5)3sin⁡(5x−x)cos⁡5(5x−x)−60(5xlog⁡(5)−1)3sin⁡3(5x−x)cos⁡3(5x−x)+48(5xlog⁡(5)−1)3sin⁡(5x−x)cos⁡5(5x−x)+(xe4xe4−1−1)3(tan⁡2(xe4xe4−1)+1)2e12(xe4−1)3+2(xe4xe4−1−1)3(tan⁡2(xe4xe4−1)+1)e12tan⁡2(xe4xe4−1)(xe4−1)3+6(xe4xe4−1−1)2(tan⁡2(xe4xe4−1)+1)e12tan⁡(xe4xe4−1)(xe4−1)3+3(xe4xe4−1−1)(tan⁡2(xe4xe4−1)+1)e12(xe4−1)3)2 \left(45 \cdot 5^{x} \left(5^{x} \log{\left(5 \right)} - 1\right) \log{\left(5 \right)}^{2} \sin^{2}{\left(5^{x} - x \right)} \cos^{4}{\left(5^{x} - x \right)} - 9 \cdot 5^{x} \left(5^{x} \log{\left(5 \right)} - 1\right) \log{\left(5 \right)}^{2} \cos^{6}{\left(5^{x} - x \right)} - 3 \cdot 5^{x} \log{\left(5 \right)}^{3} \sin{\left(5^{x} - x \right)} \cos^{5}{\left(5^{x} - x \right)} - 60 \left(5^{x} \log{\left(5 \right)} - 1\right)^{3} \sin^{3}{\left(5^{x} - x \right)} \cos^{3}{\left(5^{x} - x \right)} + 48 \left(5^{x} \log{\left(5 \right)} - 1\right)^{3} \sin{\left(5^{x} - x \right)} \cos^{5}{\left(5^{x} - x \right)} + \frac{\left(\frac{x e^{4}}{x e^{4} - 1} - 1\right)^{3} \left(\tan^{2}{\left(\frac{x e^{4}}{x e^{4} - 1} \right)} + 1\right)^{2} e^{12}}{\left(x e^{4} - 1\right)^{3}} + \frac{2 \left(\frac{x e^{4}}{x e^{4} - 1} - 1\right)^{3} \left(\tan^{2}{\left(\frac{x e^{4}}{x e^{4} - 1} \right)} + 1\right) e^{12} \tan^{2}{\left(\frac{x e^{4}}{x e^{4} - 1} \right)}}{\left(x e^{4} - 1\right)^{3}} + \frac{6 \left(\frac{x e^{4}}{x e^{4} - 1} - 1\right)^{2} \left(\tan^{2}{\left(\frac{x e^{4}}{x e^{4} - 1} \right)} + 1\right) e^{12} \tan{\left(\frac{x e^{4}}{x e^{4} - 1} \right)}}{\left(x e^{4} - 1\right)^{3}} + \frac{3 \left(\frac{x e^{4}}{x e^{4} - 1} - 1\right) \left(\tan^{2}{\left(\frac{x e^{4}}{x e^{4} - 1} \right)} + 1\right) e^{12}}{\left(x e^{4} - 1\right)^{3}}\right)
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Gráfico
Derivada de cos(5^x-x)^6+tan(e^4*x/(1-e^4*x))+tan(log(8))
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