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y=arcctg(cos(x)/x)
Derivada de la función/ cos(x)/ y=arcctg(cos(x)/x)

Derivada de y=arcctg(cos(x)/x)

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

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Solución

Ha introducido [src] 
    /cos(x)\
acot|------|
    \  x   /
acot⁡(cos⁡(x)x)\operatorname{acot}{\left(\frac{\cos{\left(x \right)}}{x} \right)} 
acot(cos(x)/x)
Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
 /  sin(x)   cos(x)\ 
-|- ------ - ------| 
 |    x         2  | 
 \             x   / 
---------------------
            2        
         cos (x)     
     1 + -------     
             2       
            x
−−sin⁡(x)x−cos⁡(x)x21+cos⁡2(x)x2- \frac{- \frac{\sin{\left(x \right)}}{x} - \frac{\cos{\left(x \right)}}{x^{2}}}{1 + \frac{\cos^{2}{\left(x \right)}}{x^{2}}}
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Segunda derivada [src] 
                                           2                
                          /cos(x)         \                 
                        2*|------ + sin(x)| *cos(x)         
  2*sin(x)   2*cos(x)     \  x            /                 
- -------- - -------- + --------------------------- + cos(x)
     x           2               /       2   \              
                x              2 |    cos (x)|              
                              x *|1 + -------|              
                                 |        2  |              
                                 \       x   /              
------------------------------------------------------------
                        /       2   \                       
                        |    cos (x)|                       
                      x*|1 + -------|                       
                        |        2  |                       
                        \       x   /
cos⁡(x)−2sin⁡(x)x−2cos⁡(x)x2+2(sin⁡(x)+cos⁡(x)x)2cos⁡(x)x2(1+cos⁡2(x)x2)x(1+cos⁡2(x)x2)\frac{\cos{\left(x \right)} - \frac{2 \sin{\left(x \right)}}{x} - \frac{2 \cos{\left(x \right)}}{x^{2}} + \frac{2 \left(\sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{x}\right)^{2} \cos{\left(x \right)}}{x^{2} \left(1 + \frac{\cos^{2}{\left(x \right)}}{x^{2}}\right)}}{x \left(1 + \frac{\cos^{2}{\left(x \right)}}{x^{2}}\right)}
Simplificar
Tercera derivada [src] 
                                                               /                         2                     \                                                                                            
                                             /cos(x)         \ |   2         2      3*cos (x)   4*cos(x)*sin(x)|                      3             /cos(x)         \ /          2*sin(x)   2*cos(x)\       
                                           2*|------ + sin(x)|*|sin (x) - cos (x) + --------- + ---------------|     /cos(x)         \     2      4*|------ + sin(x)|*|-cos(x) + -------- + --------|*cos(x)
                                             \  x            / |                         2             x       |   8*|------ + sin(x)| *cos (x)     \  x            / |             x           2   |       
          3*cos(x)   6*cos(x)   6*sin(x)                       \                        x                      /     \  x            /                                \                        x    /       
-sin(x) - -------- + -------- + -------- - --------------------------------------------------------------------- + ---------------------------- - ----------------------------------------------------------
             x           3          2                                    /       2   \                                                  2                                 /       2   \                     
                        x          x                                   2 |    cos (x)|                                     /       2   \                                2 |    cos (x)|                     
                                                                      x *|1 + -------|                                   4 |    cos (x)|                               x *|1 + -------|                     
                                                                         |        2  |                                  x *|1 + -------|                                  |        2  |                     
                                                                         \       x   /                                     |        2  |                                  \       x   /                     
                                                                                                                           \       x   /                                                                    
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                /       2   \                                                                                               
                                                                                                |    cos (x)|                                                                                               
                                                                                              x*|1 + -------|                                                                                               
                                                                                                |        2  |                                                                                               
                                                                                                \       x   /
−sin⁡(x)−3cos⁡(x)x+6sin⁡(x)x2−4(sin⁡(x)+cos⁡(x)x)(−cos⁡(x)+2sin⁡(x)x+2cos⁡(x)x2)cos⁡(x)x2(1+cos⁡2(x)x2)−2(sin⁡(x)+cos⁡(x)x)(sin⁡2(x)−cos⁡2(x)+4sin⁡(x)cos⁡(x)x+3cos⁡2(x)x2)x2(1+cos⁡2(x)x2)+6cos⁡(x)x3+8(sin⁡(x)+cos⁡(x)x)3cos⁡2(x)x4(1+cos⁡2(x)x2)2x(1+cos⁡2(x)x2)\frac{- \sin{\left(x \right)} - \frac{3 \cos{\left(x \right)}}{x} + \frac{6 \sin{\left(x \right)}}{x^{2}} - \frac{4 \left(\sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{x}\right) \left(- \cos{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{x} + \frac{2 \cos{\left(x \right)}}{x^{2}}\right) \cos{\left(x \right)}}{x^{2} \left(1 + \frac{\cos^{2}{\left(x \right)}}{x^{2}}\right)} - \frac{2 \left(\sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{x}\right) \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)} + \frac{4 \sin{\left(x \right)} \cos{\left(x \right)}}{x} + \frac{3 \cos^{2}{\left(x \right)}}{x^{2}}\right)}{x^{2} \left(1 + \frac{\cos^{2}{\left(x \right)}}{x^{2}}\right)} + \frac{6 \cos{\left(x \right)}}{x^{3}} + \frac{8 \left(\sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{x}\right)^{3} \cos^{2}{\left(x \right)}}{x^{4} \left(1 + \frac{\cos^{2}{\left(x \right)}}{x^{2}}\right)^{2}}}{x \left(1 + \frac{\cos^{2}{\left(x \right)}}{x^{2}}\right)}
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Gráfico
Derivada de y=arcctg(cos(x)/x)
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