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y=arctg((cosx)^(1/x))
Derivada de la función/ arctg/ (1/x)/ y=arctg((cosx)^(1/x))

Derivada de y=arctg((cosx)^(1/x))

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
    /x ________\
atan\\/ cos(x) /
atan⁡(cos⁡1x(x))\operatorname{atan}{\left(\cos^{\frac{1}{x}}{\left(x \right)} \right)} 
atan(cos(x)^(1/x))
Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
x ________ /  log(cos(x))    sin(x) \
\/ cos(x) *|- ----------- - --------|
           |        2       x*cos(x)|
           \       x                /
-------------------------------------
                        2            
                        -            
                        x            
            1 + (cos(x))
(−sin⁡(x)xcos⁡(x)−log⁡(cos⁡(x))x2)cos⁡1x(x)cos⁡2x(x)+1\frac{\left(- \frac{\sin{\left(x \right)}}{x \cos{\left(x \right)}} - \frac{\log{\left(\cos{\left(x \right)} \right)}}{x^{2}}\right) \cos^{\frac{1}{x}}{\left(x \right)}}{\cos^{\frac{2}{x}}{\left(x \right)} + 1}
Simplificar
Segunda derivada [src] 
           /                                                                                                      2\
           |                           2                                                                2         -|
           |     /log(cos(x))   sin(x)\                                           /log(cos(x))   sin(x)\          x|
           |     |----------- + ------|       2                                 2*|----------- + ------| *(cos(x)) |
x ________ |     \     x        cos(x)/    sin (x)   2*log(cos(x))   2*sin(x)     \     x        cos(x)/           |
\/ cos(x) *|-1 + ----------------------- - ------- + ------------- + -------- - -----------------------------------|
           |                x                 2             2        x*cos(x)              /            2\         |
           |                               cos (x)         x                               |            -|         |
           |                                                                               |            x|         |
           \                                                                             x*\1 + (cos(x)) /         /
--------------------------------------------------------------------------------------------------------------------
                                                   /            2\                                                  
                                                   |            -|                                                  
                                                   |            x|                                                  
                                                 x*\1 + (cos(x)) /
(−sin⁡2(x)cos⁡2(x)−1+(sin⁡(x)cos⁡(x)+log⁡(cos⁡(x))x)2x−2(sin⁡(x)cos⁡(x)+log⁡(cos⁡(x))x)2cos⁡2x(x)x(cos⁡2x(x)+1)+2sin⁡(x)xcos⁡(x)+2log⁡(cos⁡(x))x2)cos⁡1x(x)x(cos⁡2x(x)+1)\frac{\left(- \frac{\sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} - 1 + \frac{\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{\log{\left(\cos{\left(x \right)} \right)}}{x}\right)^{2}}{x} - \frac{2 \left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{\log{\left(\cos{\left(x \right)} \right)}}{x}\right)^{2} \cos^{\frac{2}{x}}{\left(x \right)}}{x \left(\cos^{\frac{2}{x}}{\left(x \right)} + 1\right)} + \frac{2 \sin{\left(x \right)}}{x \cos{\left(x \right)}} + \frac{2 \log{\left(\cos{\left(x \right)} \right)}}{x^{2}}\right) \cos^{\frac{1}{x}}{\left(x \right)}}{x \left(\cos^{\frac{2}{x}}{\left(x \right)} + 1\right)}
Simplificar
Tercera derivada [src] 
           /                                                                                                                                                                                                                                                       2                                                                \
           |                                                                                                                      /       2                              \                                     4                                     2             -                        /       2                              \|
           |                          3                                                                    /log(cos(x))   sin(x)\ |    sin (x)   2*log(cos(x))   2*sin(x)|                           3         -                           3         -             x /log(cos(x))   sin(x)\ |    sin (x)   2*log(cos(x))   2*sin(x)||
           |    /log(cos(x))   sin(x)\                                                                   3*|----------- + ------|*|1 + ------- - ------------- - --------|     /log(cos(x))   sin(x)\          x     /log(cos(x))   sin(x)\          x   6*(cos(x)) *|----------- + ------|*|1 + ------- - ------------- - --------||
           |    |----------- + ------|                                    3                       2        \     x        cos(x)/ |       2             2        x*cos(x)|   8*|----------- + ------| *(cos(x))    8*|----------- + ------| *(cos(x))                \     x        cos(x)/ |       2             2        x*cos(x)||
x ________ |3   \     x        cos(x)/    6*log(cos(x))   2*sin(x)   2*sin (x)    6*sin(x)   3*sin (x)                            \    cos (x)         x                 /     \     x        cos(x)/                \     x        cos(x)/                                                 \    cos (x)         x                 /|
\/ cos(x) *|- - ----------------------- - ------------- - -------- - --------- - --------- + --------- + ----------------------------------------------------------------- - ----------------------------------- + ----------------------------------- - ---------------------------------------------------------------------------|
           |x               2                    3         cos(x)        3        2               2                                      x                                                             2                       /            2\                                          /            2\                             |
           |               x                    x                     cos (x)    x *cos(x)   x*cos (x)                                                                                  /            2\                        |            -|                                          |            -|                             |
           |                                                                                                                                                                            |            -|                      2 |            x|                                          |            x|                             |
           |                                                                                                                                                                          2 |            x|                     x *\1 + (cos(x)) /                                        x*\1 + (cos(x)) /                             |
           \                                                                                                                                                                         x *\1 + (cos(x)) /                                                                                                                             /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                            /            2\                                                                                                                                                          
                                                                                                                                                            |            -|                                                                                                                                                          
                                                                                                                                                            |            x|                                                                                                                                                          
                                                                                                                                                          x*\1 + (cos(x)) /
(−2sin⁡3(x)cos⁡3(x)−2sin⁡(x)cos⁡(x)+3(sin⁡(x)cos⁡(x)+log⁡(cos⁡(x))x)(sin⁡2(x)cos⁡2(x)+1−2sin⁡(x)xcos⁡(x)−2log⁡(cos⁡(x))x2)x−6(sin⁡(x)cos⁡(x)+log⁡(cos⁡(x))x)(sin⁡2(x)cos⁡2(x)+1−2sin⁡(x)xcos⁡(x)−2log⁡(cos⁡(x))x2)cos⁡2x(x)x(cos⁡2x(x)+1)+3sin⁡2(x)xcos⁡2(x)+3x−(sin⁡(x)cos⁡(x)+log⁡(cos⁡(x))x)3x2+8(sin⁡(x)cos⁡(x)+log⁡(cos⁡(x))x)3cos⁡2x(x)x2(cos⁡2x(x)+1)−8(sin⁡(x)cos⁡(x)+log⁡(cos⁡(x))x)3cos⁡4x(x)x2(cos⁡2x(x)+1)2−6sin⁡(x)x2cos⁡(x)−6log⁡(cos⁡(x))x3)cos⁡1x(x)x(cos⁡2x(x)+1)\frac{\left(- \frac{2 \sin^{3}{\left(x \right)}}{\cos^{3}{\left(x \right)}} - \frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{3 \left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{\log{\left(\cos{\left(x \right)} \right)}}{x}\right) \left(\frac{\sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 1 - \frac{2 \sin{\left(x \right)}}{x \cos{\left(x \right)}} - \frac{2 \log{\left(\cos{\left(x \right)} \right)}}{x^{2}}\right)}{x} - \frac{6 \left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{\log{\left(\cos{\left(x \right)} \right)}}{x}\right) \left(\frac{\sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 1 - \frac{2 \sin{\left(x \right)}}{x \cos{\left(x \right)}} - \frac{2 \log{\left(\cos{\left(x \right)} \right)}}{x^{2}}\right) \cos^{\frac{2}{x}}{\left(x \right)}}{x \left(\cos^{\frac{2}{x}}{\left(x \right)} + 1\right)} + \frac{3 \sin^{2}{\left(x \right)}}{x \cos^{2}{\left(x \right)}} + \frac{3}{x} - \frac{\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{\log{\left(\cos{\left(x \right)} \right)}}{x}\right)^{3}}{x^{2}} + \frac{8 \left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{\log{\left(\cos{\left(x \right)} \right)}}{x}\right)^{3} \cos^{\frac{2}{x}}{\left(x \right)}}{x^{2} \left(\cos^{\frac{2}{x}}{\left(x \right)} + 1\right)} - \frac{8 \left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{\log{\left(\cos{\left(x \right)} \right)}}{x}\right)^{3} \cos^{\frac{4}{x}}{\left(x \right)}}{x^{2} \left(\cos^{\frac{2}{x}}{\left(x \right)} + 1\right)^{2}} - \frac{6 \sin{\left(x \right)}}{x^{2} \cos{\left(x \right)}} - \frac{6 \log{\left(\cos{\left(x \right)} \right)}}{x^{3}}\right) \cos^{\frac{1}{x}}{\left(x \right)}}{x \left(\cos^{\frac{2}{x}}{\left(x \right)} + 1\right)}
Simplificar
Gráfico
Derivada de y=arctg((cosx)^(1/x))
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