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tan(x)^(4)*asin(4*x^5)
Derivada de la función/ 4*x^5/ tan(x)/ tan(x)^(4)*asin(4*x^5)

Derivada de tan(x)^(4)*asin(4*x^5)

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

Gráfico:

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Solución

Ha introducido [src] 
   4        /   5\
tan (x)*asin\4*x /
tan⁡4(x)asin⁡(4x5)\tan^{4}{\left(x \right)} \operatorname{asin}{\left(4 x^{5} \right)} 
tan(x)^4*asin(4*x^5)
Gráfica
02468-8-6-4-2-1010-1010
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Trazar el gráfico f'(x)
Primera derivada [src] 
                                          4    4    
   3    /         2   \     /   5\    20*x *tan (x) 
tan (x)*\4 + 4*tan (x)/*asin\4*x / + ---------------
                                        ____________
                                       /         10 
                                     \/  1 - 16*x
20x4tan⁡4(x)1−16x10+(4tan⁡2(x)+4)tan⁡3(x)asin⁡(4x5)\frac{20 x^{4} \tan^{4}{\left(x \right)}}{\sqrt{1 - 16 x^{10}}} + \left(4 \tan^{2}{\left(x \right)} + 4\right) \tan^{3}{\left(x \right)} \operatorname{asin}{\left(4 x^{5} \right)}
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Segunda derivada [src] 
          /                                                         /            10  \                             \
          |                                               3    2    |        20*x    |                             |
          |                                           20*x *tan (x)*|-1 + -----------|                             |
          |                                                         |              10|       4 /       2   \       |
     2    |/       2   \ /         2   \     /   5\                 \     -1 + 16*x  /   40*x *\1 + tan (x)/*tan(x)|
4*tan (x)*|\1 + tan (x)/*\3 + 5*tan (x)/*asin\4*x / - -------------------------------- + --------------------------|
          |                                                      ____________                    ____________      |
          |                                                     /         10                    /         10       |
          \                                                   \/  1 - 16*x                    \/  1 - 16*x         /
4(40x4(tan⁡2(x)+1)tan⁡(x)1−16x10−20x3(20x1016x10−1−1)tan⁡2(x)1−16x10+(tan⁡2(x)+1)(5tan⁡2(x)+3)asin⁡(4x5))tan⁡2(x)4 \left(\frac{40 x^{4} \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{\sqrt{1 - 16 x^{10}}} - \frac{20 x^{3} \left(\frac{20 x^{10}}{16 x^{10} - 1} - 1\right) \tan^{2}{\left(x \right)}}{\sqrt{1 - 16 x^{10}}} + \left(\tan^{2}{\left(x \right)} + 1\right) \left(5 \tan^{2}{\left(x \right)} + 3\right) \operatorname{asin}{\left(4 x^{5} \right)}\right) \tan^{2}{\left(x \right)}
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Tercera derivada [src] 
  /                                                                                                   /           10              20   \                                                                                               \       
  |                                                                                         2    3    |      340*x          4800*x     |                                /            10  \                                             |       
  |                                                                                     10*x *tan (x)*|3 - ----------- + --------------|        3    2    /       2   \ |        20*x    |                                             |       
  |                                                                                                   |             10                2|   120*x *tan (x)*\1 + tan (x)/*|-1 + -----------|                                             |       
  |              /                           2                           \                            |    -1 + 16*x     /         10\ |                                |              10|       4 /       2   \ /         2   \       |       
  |/       2   \ |     4        /       2   \          2    /       2   \|     /   5\                 \                  \-1 + 16*x  / /                                \     -1 + 16*x  /   30*x *\1 + tan (x)/*\3 + 5*tan (x)/*tan(x)|       
8*|\1 + tan (x)/*\2*tan (x) + 3*\1 + tan (x)/  + 10*tan (x)*\1 + tan (x)//*asin\4*x / + ------------------------------------------------ - ----------------------------------------------- + ------------------------------------------|*tan(x)
  |                                                                                                        ____________                                       ____________                                   ____________              |       
  |                                                                                                       /         10                                       /         10                                   /         10               |       
  \                                                                                                     \/  1 - 16*x                                       \/  1 - 16*x                                   \/  1 - 16*x                 /
8(30x4(tan⁡2(x)+1)(5tan⁡2(x)+3)tan⁡(x)1−16x10−120x3(20x1016x10−1−1)(tan⁡2(x)+1)tan⁡2(x)1−16x10+10x2(4800x20(16x10−1)2−340x1016x10−1+3)tan⁡3(x)1−16x10+(tan⁡2(x)+1)(3(tan⁡2(x)+1)2+10(tan⁡2(x)+1)tan⁡2(x)+2tan⁡4(x))asin⁡(4x5))tan⁡(x)8 \left(\frac{30 x^{4} \left(\tan^{2}{\left(x \right)} + 1\right) \left(5 \tan^{2}{\left(x \right)} + 3\right) \tan{\left(x \right)}}{\sqrt{1 - 16 x^{10}}} - \frac{120 x^{3} \left(\frac{20 x^{10}}{16 x^{10} - 1} - 1\right) \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)}}{\sqrt{1 - 16 x^{10}}} + \frac{10 x^{2} \left(\frac{4800 x^{20}}{\left(16 x^{10} - 1\right)^{2}} - \frac{340 x^{10}}{16 x^{10} - 1} + 3\right) \tan^{3}{\left(x \right)}}{\sqrt{1 - 16 x^{10}}} + \left(\tan^{2}{\left(x \right)} + 1\right) \left(3 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 10 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} + 2 \tan^{4}{\left(x \right)}\right) \operatorname{asin}{\left(4 x^{5} \right)}\right) \tan{\left(x \right)}
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Gráfico
Derivada de tan(x)^(4)*asin(4*x^5)
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