Sr Examen

Otras calculadoras


y=(cos(2x))^(1/x)

Derivada de y=(cos(2x))^(1/x)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
x __________
\/ cos(2*x) 
cos1x(2x)\cos^{\frac{1}{x}}{\left(2 x \right)}
cos(2*x)^(1/x)
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

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


Respuesta:

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

Gráfica
02468-8-6-4-2-1010-250250
Primera derivada [src]
x __________ /  log(cos(2*x))   2*sin(2*x)\
\/ cos(2*x) *|- ------------- - ----------|
             |         2        x*cos(2*x)|
             \        x                   /
(2sin(2x)xcos(2x)log(cos(2x))x2)cos1x(2x)\left(- \frac{2 \sin{\left(2 x \right)}}{x \cos{\left(2 x \right)}} - \frac{\log{\left(\cos{\left(2 x \right)} \right)}}{x^{2}}\right) \cos^{\frac{1}{x}}{\left(2 x \right)}
Segunda derivada [src]
             /                                 2                                             \
             |     /log(cos(2*x))   2*sin(2*x)\                                              |
             |     |------------- + ----------|         2                                    |
x __________ |     \      x          cos(2*x) /    4*sin (2*x)   2*log(cos(2*x))   4*sin(2*x)|
\/ cos(2*x) *|-4 + ----------------------------- - ----------- + --------------- + ----------|
             |                   x                     2                 2         x*cos(2*x)|
             \                                      cos (2*x)           x                    /
----------------------------------------------------------------------------------------------
                                              x                                               
(4sin2(2x)cos2(2x)4+(2sin(2x)cos(2x)+log(cos(2x))x)2x+4sin(2x)xcos(2x)+2log(cos(2x))x2)cos1x(2x)x\frac{\left(- \frac{4 \sin^{2}{\left(2 x \right)}}{\cos^{2}{\left(2 x \right)}} - 4 + \frac{\left(\frac{2 \sin{\left(2 x \right)}}{\cos{\left(2 x \right)}} + \frac{\log{\left(\cos{\left(2 x \right)} \right)}}{x}\right)^{2}}{x} + \frac{4 \sin{\left(2 x \right)}}{x \cos{\left(2 x \right)}} + \frac{2 \log{\left(\cos{\left(2 x \right)} \right)}}{x^{2}}\right) \cos^{\frac{1}{x}}{\left(2 x \right)}}{x}
Tercera derivada [src]
             /                                                                                                                                 /                         2                  \               \
             |                                 3                                                                  /log(cos(2*x))   2*sin(2*x)\ |    log(cos(2*x))   2*sin (2*x)   2*sin(2*x)|               |
             |     /log(cos(2*x))   2*sin(2*x)\                                                                 6*|------------- + ----------|*|2 - ------------- + ----------- - ----------|               |
             |     |------------- + ----------|                        3                                          \      x          cos(2*x) / |           2            2         x*cos(2*x)|         2     |
x __________ |12   \      x          cos(2*x) /    16*sin(2*x)   16*sin (2*x)   6*log(cos(2*x))   12*sin(2*x)                                  \          x          cos (2*x)              /   12*sin (2*x)|
\/ cos(2*x) *|-- - ----------------------------- - ----------- - ------------ - --------------- - ----------- + ----------------------------------------------------------------------------- + ------------|
             |x                   2                  cos(2*x)        3                  3          2                                                  x                                              2      |
             \                   x                                cos (2*x)            x          x *cos(2*x)                                                                                   x*cos (2*x) /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                      x                                                                                                      
(16sin3(2x)cos3(2x)16sin(2x)cos(2x)+6(2sin(2x)cos(2x)+log(cos(2x))x)(2sin2(2x)cos2(2x)+22sin(2x)xcos(2x)log(cos(2x))x2)x+12sin2(2x)xcos2(2x)+12x(2sin(2x)cos(2x)+log(cos(2x))x)3x212sin(2x)x2cos(2x)6log(cos(2x))x3)cos1x(2x)x\frac{\left(- \frac{16 \sin^{3}{\left(2 x \right)}}{\cos^{3}{\left(2 x \right)}} - \frac{16 \sin{\left(2 x \right)}}{\cos{\left(2 x \right)}} + \frac{6 \left(\frac{2 \sin{\left(2 x \right)}}{\cos{\left(2 x \right)}} + \frac{\log{\left(\cos{\left(2 x \right)} \right)}}{x}\right) \left(\frac{2 \sin^{2}{\left(2 x \right)}}{\cos^{2}{\left(2 x \right)}} + 2 - \frac{2 \sin{\left(2 x \right)}}{x \cos{\left(2 x \right)}} - \frac{\log{\left(\cos{\left(2 x \right)} \right)}}{x^{2}}\right)}{x} + \frac{12 \sin^{2}{\left(2 x \right)}}{x \cos^{2}{\left(2 x \right)}} + \frac{12}{x} - \frac{\left(\frac{2 \sin{\left(2 x \right)}}{\cos{\left(2 x \right)}} + \frac{\log{\left(\cos{\left(2 x \right)} \right)}}{x}\right)^{3}}{x^{2}} - \frac{12 \sin{\left(2 x \right)}}{x^{2} \cos{\left(2 x \right)}} - \frac{6 \log{\left(\cos{\left(2 x \right)} \right)}}{x^{3}}\right) \cos^{\frac{1}{x}}{\left(2 x \right)}}{x}
Gráfico
Derivada de y=(cos(2x))^(1/x)