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x^tgx(((tgx/x)-(1/cos^2))(1/lnx))

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  • Derivada de x^-4/5 Derivada de x^-4/5
  • Derivada de x^2*5^x Derivada de x^2*5^x
  • Derivada de x/(1+e^x) Derivada de x/(1+e^x)
  • Derivada de u/v

  • Expresiones idénticas

  • x^tgx(((tgx/x)-(uno /cos^ dos))(uno /lnx))
  • x en el grado tgx(((tgx dividir por x) menos (1 dividir por coseno de al cuadrado ))(1 dividir por lnx))
  • x en el grado tgx(((tgx dividir por x) menos (uno dividir por coseno de en el grado dos))(uno dividir por lnx))
  • xtgx(((tgx/x)-(1/cos2))(1/lnx))
  • xtgxtgx/x-1/cos21/lnx
  • x^tgx(((tgx/x)-(1/cos²))(1/lnx))
  • x en el grado tgx(((tgx/x)-(1/cos en el grado 2))(1/lnx))
  • x^tgxtgx/x-1/cos^21/lnx
  • x^tgx(((tgx dividir por x)-(1 dividir por cos^2))(1 dividir por lnx))

  • Expresiones semejantes

  • x^tgx(((tgx/x)+(1/cos^2))(1/lnx))
Derivada de la función/ x^tgx(((tgx/x)-(1/cos^2))(1/lnx))

Derivada de x^tgx(((tgx/x)-(1/cos^2))(1/lnx))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
        tan(x)      1   
        ------ - -------
          x         2   
 tan(x)          cos (x)
x      *----------------
             log(x)
xtan⁡(x)−1cos⁡2(x)+tan⁡(x)xlog⁡(x)x^{\tan{\left(x \right)}} \frac{- \frac{1}{\cos^{2}{\left(x \right)}} + \frac{\tan{\left(x \right)}}{x}}{\log{\left(x \right)}} 
x^tan(x)*((tan(x)/x - 1/cos(x)^2)/log(x))
Primera derivada [src] 
        /       2                                          \                                                             
        |1 + tan (x)   tan(x)   2*sin(x)   tan(x)      1   |    tan(x) /tan(x)   /       2   \       \ /tan(x)      1   \
        |----------- - ------ - --------   ------ - -------|   x      *|------ + \1 + tan (x)/*log(x)|*|------ - -------|
        |     x           2        3         x         2   |           \  x                          / |  x         2   |
 tan(x) |                x      cos (x)             cos (x)|                                           \         cos (x)/
x      *|------------------------------- - ----------------| + ----------------------------------------------------------
        |             log(x)                       2       |                             log(x)                          
        \                                     x*log (x)    /
xtan⁡(x)((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)(−1cos⁡2(x)+tan⁡(x)x)log⁡(x)+xtan⁡(x)(−2sin⁡(x)cos⁡3(x)+tan⁡2(x)+1x−tan⁡(x)x2log⁡(x)−−1cos⁡2(x)+tan⁡(x)xxlog⁡(x)2)\frac{x^{\tan{\left(x \right)}} \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right) \left(- \frac{1}{\cos^{2}{\left(x \right)}} + \frac{\tan{\left(x \right)}}{x}\right)}{\log{\left(x \right)}} + x^{\tan{\left(x \right)}} \left(\frac{- \frac{2 \sin{\left(x \right)}}{\cos^{3}{\left(x \right)}} + \frac{\tan^{2}{\left(x \right)} + 1}{x} - \frac{\tan{\left(x \right)}}{x^{2}}}{\log{\left(x \right)}} - \frac{- \frac{1}{\cos^{2}{\left(x \right)}} + \frac{\tan{\left(x \right)}}{x}}{x \log{\left(x \right)}^{2}}\right)
Simplificar
Segunda derivada [src] 
         /                                                                                                                                                                                                                                                                   /                2              \                                                           \ 
         |                                                                                                                                                                                            /                                       1      tan(x)\                 |tan(x)   1 + tan (x)   2*sin(x)|                            /      2   \ /   1      tan(x)\| 
         |                                                                                                                                                                                            |                                  - ------- + ------|               2*|------ - ----------- + --------|                            |1 + ------|*|------- - ------|| 
         |                             /                               2              /       2   \                                \                /       2   \                                     |                2                      2        x   |        2        |   2          x           3    |     /       2   \          \    log(x)/ |   2        x   || 
  tan(x) |   2      /   1      tan(x)\ |/tan(x)   /       2   \       \    tan(x)   2*\1 + tan (x)/     /       2   \              |   2*tan(x)   2*\1 + tan (x)/     /tan(x)   /       2   \       \ |tan(x)   1 + tan (x)   2*sin(x)     cos (x)         |   6*sin (x)     \  x                    cos (x) /   2*\1 + tan (x)/*tan(x)                \cos (x)         /| 
-x      *|------- + |------- - ------|*||------ + \1 + tan (x)/*log(x)|  - ------ + --------------- + 2*\1 + tan (x)/*log(x)*tan(x)| - -------- + --------------- + 2*|------ + \1 + tan (x)/*log(x)|*|------ - ----------- + -------- + ------------------| + --------- - ----------------------------------- - ---------------------- + -------------------------------| 
         |   2      |   2        x   | |\  x                          /       2            x                                       |       3              2           \  x                          / |   2          x           3            x*log(x)     |       4                     x*log(x)                          x                          2                  | 
         \cos (x)   \cos (x)         / \                                     x                                                     /      x              x                                            \  x                    cos (x)                      /    cos (x)                                                                              x *log(x)           / 
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                   log(x)
−xtan⁡(x)(2((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)(2sin⁡(x)cos⁡3(x)+−1cos⁡2(x)+tan⁡(x)xxlog⁡(x)−tan⁡2(x)+1x+tan⁡(x)x2)+(1cos⁡2(x)−tan⁡(x)x)(((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)2+2(tan⁡2(x)+1)log⁡(x)tan⁡(x)+2(tan⁡2(x)+1)x−tan⁡(x)x2)+6sin⁡2(x)cos⁡4(x)+2cos⁡2(x)−2(tan⁡2(x)+1)tan⁡(x)x−2(2sin⁡(x)cos⁡3(x)−tan⁡2(x)+1x+tan⁡(x)x2)xlog⁡(x)+(1+2log⁡(x))(1cos⁡2(x)−tan⁡(x)x)x2log⁡(x)+2(tan⁡2(x)+1)x2−2tan⁡(x)x3)log⁡(x)- \frac{x^{\tan{\left(x \right)}} \left(2 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right) \left(\frac{2 \sin{\left(x \right)}}{\cos^{3}{\left(x \right)}} + \frac{- \frac{1}{\cos^{2}{\left(x \right)}} + \frac{\tan{\left(x \right)}}{x}}{x \log{\left(x \right)}} - \frac{\tan^{2}{\left(x \right)} + 1}{x} + \frac{\tan{\left(x \right)}}{x^{2}}\right) + \left(\frac{1}{\cos^{2}{\left(x \right)}} - \frac{\tan{\left(x \right)}}{x}\right) \left(\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{2} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x} - \frac{\tan{\left(x \right)}}{x^{2}}\right) + \frac{6 \sin^{2}{\left(x \right)}}{\cos^{4}{\left(x \right)}} + \frac{2}{\cos^{2}{\left(x \right)}} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x} - \frac{2 \left(\frac{2 \sin{\left(x \right)}}{\cos^{3}{\left(x \right)}} - \frac{\tan^{2}{\left(x \right)} + 1}{x} + \frac{\tan{\left(x \right)}}{x^{2}}\right)}{x \log{\left(x \right)}} + \frac{\left(1 + \frac{2}{\log{\left(x \right)}}\right) \left(\frac{1}{\cos^{2}{\left(x \right)}} - \frac{\tan{\left(x \right)}}{x}\right)}{x^{2} \log{\left(x \right)}} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{2}} - \frac{2 \tan{\left(x \right)}}{x^{3}}\right)}{\log{\left(x \right)}}
Simplificar
Tercera derivada [src] 
         /                                                                                                                                                                                                                                                                                                                                                 /                                                     /                2              \                                                           \                                                                                                                                                                                                  /                 2                    2      /       2   \       \                                                                                                                   /                2              \\ 
         |                                                                                                                                                                                                                                                                                                                                                 |                                                     |tan(x)   1 + tan (x)   2*sin(x)|                            /      2   \ /   1      tan(x)\|                                                                                                   /                                       1      tan(x)\                                         |   1      1 + tan (x)   tan(x)   3*sin (x)   \1 + tan (x)/*tan(x)|                                                        /   1      tan(x)\ /      3         3   \     /      2   \ |tan(x)   1 + tan (x)   2*sin(x)|| 
         |                                                                                                                                                                                                                                                                                                           2                                     |                                                   2*|------ - ----------- + --------|                            |1 + ------|*|------- - ------||                                                                                                   |                                  - ------- + ------|                                       6*|------- + ----------- - ------ + --------- - --------------------|                                                      2*|------- - ------|*|1 + ------ + -------|   3*|1 + ------|*|------ - ----------- + --------|| 
         |                   /                               3     /       2   \                             2                                            /             /       2   \                                \                                      /       2   \       \     /       2   \     /       2   \                                      |                       /       2   \        2        |   2          x           3    |     /       2   \          \    log(x)/ |   2        x   ||     /                               2              /       2   \                                \ |                2                      2        x   |                                3        |   2            2          3         4                x          |        2    /       2   \     /       2   \            |   2        x   | |    log(x)      2   |     \    log(x)/ |   2          x           3    || 
  tan(x) |/   1      tan(x)\ |/tan(x)   /       2   \       \    3*\1 + tan (x)/   2*tan(x)     /       2   \             /tan(x)   /       2   \       \ |  tan(x)   2*\1 + tan (x)/     /       2   \              |        2    /       2   \          6*\1 + tan (x)/*tan(x)|   6*\1 + tan (x)/   2*\1 + tan (x)/      /tan(x)   /       2   \       \ |   2      2*tan(x)   2*\1 + tan (x)/   6*sin (x)     \  x                    cos (x) /   2*\1 + tan (x)/*tan(x)                \cos (x)         /|     |/tan(x)   /       2   \       \    tan(x)   2*\1 + tan (x)/     /       2   \              | |tan(x)   1 + tan (x)   2*sin(x)     cos (x)         |   6*tan(x)   16*sin(x)   24*sin (x)     \cos (x)        x          x       cos (x)                        /   4*tan (x)*\1 + tan (x)/   6*\1 + tan (x)/*tan(x)     \cos (x)         / \             log (x)/                  \  x                    cos (x) /| 
-x      *||------- - ------|*||------ + \1 + tan (x)/*log(x)|  - --------------- + -------- + 2*\1 + tan (x)/ *log(x) + 3*|------ + \1 + tan (x)/*log(x)|*|- ------ + --------------- + 2*\1 + tan (x)/*log(x)*tan(x)| + 4*tan (x)*\1 + tan (x)/*log(x) + ----------------------| - --------------- - ---------------- + 3*|------ + \1 + tan (x)/*log(x)|*|------- - -------- + --------------- + --------- - ----------------------------------- - ---------------------- + -------------------------------| + 3*||------ + \1 + tan (x)/*log(x)|  - ------ + --------------- + 2*\1 + tan (x)/*log(x)*tan(x)|*|------ - ----------- + -------- + ------------------| + -------- + --------- + ---------- - --------------------------------------------------------------------- - ----------------------- + ---------------------- - ------------------------------------------- + ------------------------------------------------| 
         ||   2        x   | |\  x                          /            2             3                                  \  x                          / |     2            x                                       |                                              x           |           3                x             \  x                          / |   2          3              2             4                     x*log(x)                          x                          2                  |     |\  x                          /       2            x                                       | |   2          x           3            x*log(x)     |       4          3           5                                       x*log(x)                                            x                         2                               3                                               2                           | 
         \\cos (x)         / \                                          x             x                                                                   \    x                                                     /                                                          /          x                                                               \cos (x)      x              x           cos (x)                                                                              x *log(x)           /     \                                     x                                                     / \  x                    cos (x)                      /      x        cos (x)     cos (x)                                                                                                                 x                               x *log(x)                                       x *log(x)                    / 
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                                                                                                                                                                                                                                  log(x)
−xtan⁡(x)(3((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)(6sin⁡2(x)cos⁡4(x)+2cos⁡2(x)−2(tan⁡2(x)+1)tan⁡(x)x−2(2sin⁡(x)cos⁡3(x)−tan⁡2(x)+1x+tan⁡(x)x2)xlog⁡(x)+(1+2log⁡(x))(1cos⁡2(x)−tan⁡(x)x)x2log⁡(x)+2(tan⁡2(x)+1)x2−2tan⁡(x)x3)+(1cos⁡2(x)−tan⁡(x)x)(((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)3+3((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)(2(tan⁡2(x)+1)log⁡(x)tan⁡(x)+2(tan⁡2(x)+1)x−tan⁡(x)x2)+2(tan⁡2(x)+1)2log⁡(x)+4(tan⁡2(x)+1)log⁡(x)tan⁡2(x)+6(tan⁡2(x)+1)tan⁡(x)x−3(tan⁡2(x)+1)x2+2tan⁡(x)x3)+3(2sin⁡(x)cos⁡3(x)+−1cos⁡2(x)+tan⁡(x)xxlog⁡(x)−tan⁡2(x)+1x+tan⁡(x)x2)(((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)2+2(tan⁡2(x)+1)log⁡(x)tan⁡(x)+2(tan⁡2(x)+1)x−tan⁡(x)x2)+24sin⁡3(x)cos⁡5(x)+16sin⁡(x)cos⁡3(x)−2(tan⁡2(x)+1)2x−4(tan⁡2(x)+1)tan⁡2(x)x−6(3sin⁡2(x)cos⁡4(x)+1cos⁡2(x)−(tan⁡2(x)+1)tan⁡(x)x+tan⁡2(x)+1x2−tan⁡(x)x3)xlog⁡(x)+3(1+2log⁡(x))(2sin⁡(x)cos⁡3(x)−tan⁡2(x)+1x+tan⁡(x)x2)x2log⁡(x)+6(tan⁡2(x)+1)tan⁡(x)x2−2(1cos⁡2(x)−tan⁡(x)x)(1+3log⁡(x)+3log⁡(x)2)x3log⁡(x)−6(tan⁡2(x)+1)x3+6tan⁡(x)x4)log⁡(x)- \frac{x^{\tan{\left(x \right)}} \left(3 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right) \left(\frac{6 \sin^{2}{\left(x \right)}}{\cos^{4}{\left(x \right)}} + \frac{2}{\cos^{2}{\left(x \right)}} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x} - \frac{2 \left(\frac{2 \sin{\left(x \right)}}{\cos^{3}{\left(x \right)}} - \frac{\tan^{2}{\left(x \right)} + 1}{x} + \frac{\tan{\left(x \right)}}{x^{2}}\right)}{x \log{\left(x \right)}} + \frac{\left(1 + \frac{2}{\log{\left(x \right)}}\right) \left(\frac{1}{\cos^{2}{\left(x \right)}} - \frac{\tan{\left(x \right)}}{x}\right)}{x^{2} \log{\left(x \right)}} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{2}} - \frac{2 \tan{\left(x \right)}}{x^{3}}\right) + \left(\frac{1}{\cos^{2}{\left(x \right)}} - \frac{\tan{\left(x \right)}}{x}\right) \left(\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{3} + 3 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right) \left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x} - \frac{\tan{\left(x \right)}}{x^{2}}\right) + 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan^{2}{\left(x \right)} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{2}} + \frac{2 \tan{\left(x \right)}}{x^{3}}\right) + 3 \left(\frac{2 \sin{\left(x \right)}}{\cos^{3}{\left(x \right)}} + \frac{- \frac{1}{\cos^{2}{\left(x \right)}} + \frac{\tan{\left(x \right)}}{x}}{x \log{\left(x \right)}} - \frac{\tan^{2}{\left(x \right)} + 1}{x} + \frac{\tan{\left(x \right)}}{x^{2}}\right) \left(\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{2} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x} - \frac{\tan{\left(x \right)}}{x^{2}}\right) + \frac{24 \sin^{3}{\left(x \right)}}{\cos^{5}{\left(x \right)}} + \frac{16 \sin{\left(x \right)}}{\cos^{3}{\left(x \right)}} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{x} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)}}{x} - \frac{6 \left(\frac{3 \sin^{2}{\left(x \right)}}{\cos^{4}{\left(x \right)}} + \frac{1}{\cos^{2}{\left(x \right)}} - \frac{\left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x} + \frac{\tan^{2}{\left(x \right)} + 1}{x^{2}} - \frac{\tan{\left(x \right)}}{x^{3}}\right)}{x \log{\left(x \right)}} + \frac{3 \left(1 + \frac{2}{\log{\left(x \right)}}\right) \left(\frac{2 \sin{\left(x \right)}}{\cos^{3}{\left(x \right)}} - \frac{\tan^{2}{\left(x \right)} + 1}{x} + \frac{\tan{\left(x \right)}}{x^{2}}\right)}{x^{2} \log{\left(x \right)}} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x^{2}} - \frac{2 \left(\frac{1}{\cos^{2}{\left(x \right)}} - \frac{\tan{\left(x \right)}}{x}\right) \left(1 + \frac{3}{\log{\left(x \right)}} + \frac{3}{\log{\left(x \right)}^{2}}\right)}{x^{3} \log{\left(x \right)}} - \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{3}} + \frac{6 \tan{\left(x \right)}}{x^{4}}\right)}{\log{\left(x \right)}}
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Gráfico
Derivada de x^tgx(((tgx/x)-(1/cos^2))(1/lnx))
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