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Derivada de la función/ tg^2x/ sqrt5x/ y=asin(sqrt5x*tg^2x)

Derivada de y=asin(sqrt5x*tg^2x)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
    /  _____    2   \
asin\\/ 5*x *tan (x)/
asin⁡(5xtan⁡2(x))\operatorname{asin}{\left(\sqrt{5 x} \tan^{2}{\left(x \right)} \right)} 
asin(sqrt(5*x)*tan(x)^2)
Gráfica
02468-8-6-4-2-1010-1010
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Trazar el gráfico f'(x)
Primera derivada [src] 
                                       ___    2   
  ___   ___ /         2   \          \/ 5 *tan (x)
\/ 5 *\/ x *\2 + 2*tan (x)/*tan(x) + -------------
                                            ___   
                                        2*\/ x    
--------------------------------------------------
                  _________________               
                 /            4                   
               \/  1 - 5*x*tan (x)
5x(2tan⁡2(x)+2)tan⁡(x)+5tan⁡2(x)2x−5xtan⁡4(x)+1\frac{\sqrt{5} \sqrt{x} \left(2 \tan^{2}{\left(x \right)} + 2\right) \tan{\left(x \right)} + \frac{\sqrt{5} \tan^{2}{\left(x \right)}}{2 \sqrt{x}}}{\sqrt{- 5 x \tan^{4}{\left(x \right)} + 1}}
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Segunda derivada [src] 
      /                                                                                                 4    /tan(x)       ___ /       2   \\ /    /       2   \         \\
      |                                                                                            5*tan (x)*|------ + 4*\/ x *\1 + tan (x)/|*\4*x*\1 + tan (x)/ + tan(x)/|
      |                     2      2        /       2   \                                                    |  ___                         |                             |
  ___ |    ___ /       2   \    tan (x)   2*\1 + tan (x)/*tan(x)       ___    2    /       2   \             \\/ x                          /                             |
\/ 5 *|2*\/ x *\1 + tan (x)/  - ------- + ---------------------- + 4*\/ x *tan (x)*\1 + tan (x)/ + -----------------------------------------------------------------------|
      |                             3/2             ___                                                                        /           4   \                          |
      \                          4*x              \/ x                                                                       4*\1 - 5*x*tan (x)/                          /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                               _________________                                                                           
                                                                              /            4                                                                               
                                                                            \/  1 - 5*x*tan (x)
5(2x(tan⁡2(x)+1)2+4x(tan⁡2(x)+1)tan⁡2(x)+5(4x(tan⁡2(x)+1)+tan⁡(x)x)(4x(tan⁡2(x)+1)+tan⁡(x))tan⁡4(x)4(−5xtan⁡4(x)+1)+2(tan⁡2(x)+1)tan⁡(x)x−tan⁡2(x)4x32)−5xtan⁡4(x)+1\frac{\sqrt{5} \left(2 \sqrt{x} \left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 4 \sqrt{x} \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} + \frac{5 \left(4 \sqrt{x} \left(\tan^{2}{\left(x \right)} + 1\right) + \frac{\tan{\left(x \right)}}{\sqrt{x}}\right) \left(4 x \left(\tan^{2}{\left(x \right)} + 1\right) + \tan{\left(x \right)}\right) \tan^{4}{\left(x \right)}}{4 \left(- 5 x \tan^{4}{\left(x \right)} + 1\right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{\sqrt{x}} - \frac{\tan^{2}{\left(x \right)}}{4 x^{\frac{3}{2}}}\right)}{\sqrt{- 5 x \tan^{4}{\left(x \right)} + 1}}
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Tercera derivada [src] 
      /                                                                                                                                                                                          /     2                           2     /       2   \                                        \                                  2                                                                                                                                                 \
      |                                                                                                                                                        3    /    /       2   \         \ |  tan (x)       ___ /       2   \    8*\1 + tan (x)/*tan(x)        ___    2    /       2   \|      /    /       2   \         \     7    /tan(x)       ___ /       2   \\        3    /       2   \ /tan(x)       ___ /       2   \\ /                  2          /       2   \\|
      |               2                                                                                                                                   5*tan (x)*\4*x*\1 + tan (x)/ + tan(x)/*|- ------- + 8*\/ x *\1 + tan (x)/  + ---------------------- + 16*\/ x *tan (x)*\1 + tan (x)/|   75*\4*x*\1 + tan (x)/ + tan(x)/ *tan (x)*|------ + 4*\/ x *\1 + tan (x)/|   5*tan (x)*\1 + tan (x)/*|------ + 4*\/ x *\1 + tan (x)/|*\2*tan(x) + 2*x*tan (x) + 3*x*\1 + tan (x)//|
      |  /       2   \         2           2    /       2   \                                                         2            /       2   \                                                 |     3/2                                       ___                                          |                                            |  ___                         |                           |  ___                         |                                             |
  ___ |3*\1 + tan (x)/    3*tan (x)   6*tan (x)*\1 + tan (x)/       ___    3    /       2   \        ___ /       2   \           3*\1 + tan (x)/*tan(x)                                          \    x                                        \/ x                                           /                                            \\/ x                          /                           \\/ x                          /                                             |
\/ 5 *|---------------- + --------- + ----------------------- + 8*\/ x *tan (x)*\1 + tan (x)/ + 16*\/ x *\1 + tan (x)/ *tan(x) - ---------------------- + ------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------|
      |       ___              5/2               ___                                                                                        3/2                                                                      /           4   \                                                                                                          2                                                                                   4                                              |
      |     \/ x            8*x                \/ x                                                                                      2*x                                                                       4*\1 - 5*x*tan (x)/                                                                                         /           4   \                                                                         1 - 5*x*tan (x)                                           |
      \                                                                                                                                                                                                                                                                                                                      8*\1 - 5*x*tan (x)/                                                                                                                                   /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                   _________________                                                                                                                                                                                                                                
                                                                                                                                                                                                                                  /            4                                                                                                                                                                                                                                    
                                                                                                                                                                                                                                \/  1 - 5*x*tan (x)
5(16x(tan⁡2(x)+1)2tan⁡(x)+8x(tan⁡2(x)+1)tan⁡3(x)+75(4x(tan⁡2(x)+1)+tan⁡(x)x)(4x(tan⁡2(x)+1)+tan⁡(x))2tan⁡7(x)8(−5xtan⁡4(x)+1)2+5(4x(tan⁡2(x)+1)+tan⁡(x)x)(tan⁡2(x)+1)(3x(tan⁡2(x)+1)+2xtan⁡2(x)+2tan⁡(x))tan⁡3(x)−5xtan⁡4(x)+1+5(4x(tan⁡2(x)+1)+tan⁡(x))(8x(tan⁡2(x)+1)2+16x(tan⁡2(x)+1)tan⁡2(x)+8(tan⁡2(x)+1)tan⁡(x)x−tan⁡2(x)x32)tan⁡3(x)4(−5xtan⁡4(x)+1)+3(tan⁡2(x)+1)2x+6(tan⁡2(x)+1)tan⁡2(x)x−3(tan⁡2(x)+1)tan⁡(x)2x32+3tan⁡2(x)8x52)−5xtan⁡4(x)+1\frac{\sqrt{5} \left(16 \sqrt{x} \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \tan{\left(x \right)} + 8 \sqrt{x} \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{3}{\left(x \right)} + \frac{75 \left(4 \sqrt{x} \left(\tan^{2}{\left(x \right)} + 1\right) + \frac{\tan{\left(x \right)}}{\sqrt{x}}\right) \left(4 x \left(\tan^{2}{\left(x \right)} + 1\right) + \tan{\left(x \right)}\right)^{2} \tan^{7}{\left(x \right)}}{8 \left(- 5 x \tan^{4}{\left(x \right)} + 1\right)^{2}} + \frac{5 \left(4 \sqrt{x} \left(\tan^{2}{\left(x \right)} + 1\right) + \frac{\tan{\left(x \right)}}{\sqrt{x}}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \left(3 x \left(\tan^{2}{\left(x \right)} + 1\right) + 2 x \tan^{2}{\left(x \right)} + 2 \tan{\left(x \right)}\right) \tan^{3}{\left(x \right)}}{- 5 x \tan^{4}{\left(x \right)} + 1} + \frac{5 \left(4 x \left(\tan^{2}{\left(x \right)} + 1\right) + \tan{\left(x \right)}\right) \left(8 \sqrt{x} \left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 16 \sqrt{x} \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} + \frac{8 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{\sqrt{x}} - \frac{\tan^{2}{\left(x \right)}}{x^{\frac{3}{2}}}\right) \tan^{3}{\left(x \right)}}{4 \left(- 5 x \tan^{4}{\left(x \right)} + 1\right)} + \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\sqrt{x}} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)}}{\sqrt{x}} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{2 x^{\frac{3}{2}}} + \frac{3 \tan^{2}{\left(x \right)}}{8 x^{\frac{5}{2}}}\right)}{\sqrt{- 5 x \tan^{4}{\left(x \right)} + 1}}
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