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y=(tg(2x+1))^(3/x)

Derivada de y=(tg(2x+1))^(3/x)

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src]
              3
              -
              x
(tan(2*x + 1)) 
tan3x(2x+1)\tan^{\frac{3}{x}}{\left(2 x + 1 \right)}
tan(2*x + 1)^(3/x)
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

    (3x)3x(log(3x)+1)\left(\frac{3}{x}\right)^{\frac{3}{x}} \left(\log{\left(\frac{3}{x} \right)} + 1\right)


Respuesta:

(3x)3x(log(3x)+1)\left(\frac{3}{x}\right)^{\frac{3}{x}} \left(\log{\left(\frac{3}{x} \right)} + 1\right)

Gráfica
02468-8-6-4-2-1010-200000000000000200000000000000
Primera derivada [src]
              3                                                  
              - /                          /         2         \\
              x |  3*log(tan(2*x + 1))   3*\2 + 2*tan (2*x + 1)/|
(tan(2*x + 1)) *|- ------------------- + -----------------------|
                |            2                x*tan(2*x + 1)    |
                \           x                                   /
(3(2tan2(2x+1)+2)xtan(2x+1)3log(tan(2x+1))x2)tan3x(2x+1)\left(\frac{3 \left(2 \tan^{2}{\left(2 x + 1 \right)} + 2\right)}{x \tan{\left(2 x + 1 \right)}} - \frac{3 \log{\left(\tan{\left(2 x + 1 \right)} \right)}}{x^{2}}\right) \tan^{\frac{3}{x}}{\left(2 x + 1 \right)}
Segunda derivada [src]
                  /                                                                                                                    2                        \
                  |                                                                       /                        /       2         \\                         |
                3 |                                           2                           |  log(tan(1 + 2*x))   2*\1 + tan (1 + 2*x)/|                         |
                - |                        /       2         \                          3*|- ----------------- + ---------------------|      /       2         \|
                x |         2            4*\1 + tan (1 + 2*x)/    2*log(tan(1 + 2*x))     \          x                tan(1 + 2*x)    /    4*\1 + tan (1 + 2*x)/|
3*(tan(1 + 2*x)) *|8 + 8*tan (1 + 2*x) - ---------------------- + ------------------- + ------------------------------------------------ - ---------------------|
                  |                             2                           2                                  x                               x*tan(1 + 2*x)   |
                  \                          tan (1 + 2*x)                 x                                                                                    /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                x                                                                                
3(4(tan2(2x+1)+1)2tan2(2x+1)+8tan2(2x+1)+8+3(2(tan2(2x+1)+1)tan(2x+1)log(tan(2x+1))x)2x4(tan2(2x+1)+1)xtan(2x+1)+2log(tan(2x+1))x2)tan3x(2x+1)x\frac{3 \left(- \frac{4 \left(\tan^{2}{\left(2 x + 1 \right)} + 1\right)^{2}}{\tan^{2}{\left(2 x + 1 \right)}} + 8 \tan^{2}{\left(2 x + 1 \right)} + 8 + \frac{3 \left(\frac{2 \left(\tan^{2}{\left(2 x + 1 \right)} + 1\right)}{\tan{\left(2 x + 1 \right)}} - \frac{\log{\left(\tan{\left(2 x + 1 \right)} \right)}}{x}\right)^{2}}{x} - \frac{4 \left(\tan^{2}{\left(2 x + 1 \right)} + 1\right)}{x \tan{\left(2 x + 1 \right)}} + \frac{2 \log{\left(\tan{\left(2 x + 1 \right)} \right)}}{x^{2}}\right) \tan^{\frac{3}{x}}{\left(2 x + 1 \right)}}{x}
Tercera derivada [src]
                  /                                                                                                                                                                                                                                               /                                                                2                        \                                                   \
                  |                                                                                                                          3                                                                      /                        /       2         \\ |                                             /       2         \      /       2         \|                                                   |
                  |                                                                             /                        /       2         \\                                                                       |  log(tan(1 + 2*x))   2*\1 + tan (1 + 2*x)/| |          2            log(tan(1 + 2*x))   2*\1 + tan (1 + 2*x)/    2*\1 + tan (1 + 2*x)/|                                                   |
                3 |                        2                                                    |  log(tan(1 + 2*x))   2*\1 + tan (1 + 2*x)/|                          3                                         18*|- ----------------- + ---------------------|*|-4 - 4*tan (1 + 2*x) - ----------------- + ---------------------- + ---------------------|                         2                         |
                - |     /       2         \       /       2         \                         9*|- ----------------- + ---------------------|       /       2         \                                             \          x                tan(1 + 2*x)    / |                                2                 2                     x*tan(1 + 2*x)   |      /       2         \       /       2         \|
                x |  32*\1 + tan (1 + 2*x)/    24*\1 + tan (1 + 2*x)/   6*log(tan(1 + 2*x))     \          x                tan(1 + 2*x)    /    16*\1 + tan (1 + 2*x)/       /       2         \                                                                 \                               x               tan (1 + 2*x)                             /   12*\1 + tan (1 + 2*x)/    12*\1 + tan (1 + 2*x)/|
3*(tan(1 + 2*x)) *|- ----------------------- - ---------------------- - ------------------- + ------------------------------------------------ + ----------------------- + 32*\1 + tan (1 + 2*x)/*tan(1 + 2*x) - -------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------- + ----------------------|
                  |        tan(1 + 2*x)                  x                        3                                   2                                  3                                                                                                                            x                                                                                  2                    2                 |
                  \                                                              x                                   x                                tan (1 + 2*x)                                                                                                                                                                                                 x*tan (1 + 2*x)          x *tan(1 + 2*x)    /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                        x                                                                                                                                                                                                        
3(16(tan2(2x+1)+1)3tan3(2x+1)32(tan2(2x+1)+1)2tan(2x+1)+32(tan2(2x+1)+1)tan(2x+1)18(2(tan2(2x+1)+1)tan(2x+1)log(tan(2x+1))x)(2(tan2(2x+1)+1)2tan2(2x+1)4tan2(2x+1)4+2(tan2(2x+1)+1)xtan(2x+1)log(tan(2x+1))x2)x+12(tan2(2x+1)+1)2xtan2(2x+1)24(tan2(2x+1)+1)x+9(2(tan2(2x+1)+1)tan(2x+1)log(tan(2x+1))x)3x2+12(tan2(2x+1)+1)x2tan(2x+1)6log(tan(2x+1))x3)tan3x(2x+1)x\frac{3 \left(\frac{16 \left(\tan^{2}{\left(2 x + 1 \right)} + 1\right)^{3}}{\tan^{3}{\left(2 x + 1 \right)}} - \frac{32 \left(\tan^{2}{\left(2 x + 1 \right)} + 1\right)^{2}}{\tan{\left(2 x + 1 \right)}} + 32 \left(\tan^{2}{\left(2 x + 1 \right)} + 1\right) \tan{\left(2 x + 1 \right)} - \frac{18 \left(\frac{2 \left(\tan^{2}{\left(2 x + 1 \right)} + 1\right)}{\tan{\left(2 x + 1 \right)}} - \frac{\log{\left(\tan{\left(2 x + 1 \right)} \right)}}{x}\right) \left(\frac{2 \left(\tan^{2}{\left(2 x + 1 \right)} + 1\right)^{2}}{\tan^{2}{\left(2 x + 1 \right)}} - 4 \tan^{2}{\left(2 x + 1 \right)} - 4 + \frac{2 \left(\tan^{2}{\left(2 x + 1 \right)} + 1\right)}{x \tan{\left(2 x + 1 \right)}} - \frac{\log{\left(\tan{\left(2 x + 1 \right)} \right)}}{x^{2}}\right)}{x} + \frac{12 \left(\tan^{2}{\left(2 x + 1 \right)} + 1\right)^{2}}{x \tan^{2}{\left(2 x + 1 \right)}} - \frac{24 \left(\tan^{2}{\left(2 x + 1 \right)} + 1\right)}{x} + \frac{9 \left(\frac{2 \left(\tan^{2}{\left(2 x + 1 \right)} + 1\right)}{\tan{\left(2 x + 1 \right)}} - \frac{\log{\left(\tan{\left(2 x + 1 \right)} \right)}}{x}\right)^{3}}{x^{2}} + \frac{12 \left(\tan^{2}{\left(2 x + 1 \right)} + 1\right)}{x^{2} \tan{\left(2 x + 1 \right)}} - \frac{6 \log{\left(\tan{\left(2 x + 1 \right)} \right)}}{x^{3}}\right) \tan^{\frac{3}{x}}{\left(2 x + 1 \right)}}{x}
Gráfico
Derivada de y=(tg(2x+1))^(3/x)