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asin(sin(t)/cos(t))
Derivada de la función/ sin(t)/ cos(t)/ asin(sin(t)/cos(t))

Derivada de asin(sin(t)/cos(t))

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
    /sin(t)\
asin|------|
    \cos(t)/
asin⁡(sin⁡(t)cos⁡(t))\operatorname{asin}{\left(\frac{\sin{\left(t \right)}}{\cos{\left(t \right)}} \right)} 
asin(sin(t)/cos(t))
Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
           2       
        sin (t)    
    1 + -------    
           2       
        cos (t)    
-------------------
      _____________
     /        2    
    /      sin (t) 
   /   1 - ------- 
  /           2    
\/         cos (t)
sin⁡2(t)cos⁡2(t)+1−sin⁡2(t)cos⁡2(t)+1\frac{\frac{\sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1}{\sqrt{- \frac{\sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1}}
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Segunda derivada [src] 
              /           2   \       
              |        sin (t)|       
              |    1 + -------|       
/       2   \ |           2   |       
|    sin (t)| |        cos (t)|       
|1 + -------|*|2 + -----------|*sin(t)
|       2   | |           2   |       
\    cos (t)/ |        sin (t)|       
              |    1 - -------|       
              |           2   |       
              \        cos (t)/       
--------------------------------------
            _____________             
           /        2                 
          /      sin (t)              
         /   1 - ------- *cos(t)      
        /           2                 
      \/         cos (t)
(2+sin⁡2(t)cos⁡2(t)+1−sin⁡2(t)cos⁡2(t)+1)(sin⁡2(t)cos⁡2(t)+1)sin⁡(t)−sin⁡2(t)cos⁡2(t)+1cos⁡(t)\frac{\left(2 + \frac{\frac{\sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1}{- \frac{\sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1}\right) \left(\frac{\sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1\right) \sin{\left(t \right)}}{\sqrt{- \frac{\sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1} \cos{\left(t \right)}}
Simplificar
Tercera derivada [src] 
                                                                                       3                          2        
                            /       2   \ /         4           2   \     /       2   \              /       2   \         
                            |    sin (t)| |    3*sin (t)   4*sin (t)|     |    sin (t)|     2        |    sin (t)|     2   
                            |1 + -------|*|1 + --------- + ---------|   3*|1 + -------| *sin (t)   4*|1 + -------| *sin (t)
         4           2      |       2   | |        4           2    |     |       2   |              |       2   |         
    6*sin (t)   8*sin (t)   \    cos (t)/ \     cos (t)     cos (t) /     \    cos (t)/              \    cos (t)/         
2 + --------- + --------- + ----------------------------------------- + ------------------------ + ------------------------
        4           2                             2                                   2             /       2   \          
     cos (t)     cos (t)                       sin (t)                   /       2   \              |    sin (t)|    2     
                                           1 - -------                   |    sin (t)|     2        |1 - -------|*cos (t)  
                                                  2                      |1 - -------| *cos (t)     |       2   |          
                                               cos (t)                   |       2   |              \    cos (t)/          
                                                                         \    cos (t)/                                     
---------------------------------------------------------------------------------------------------------------------------
                                                          _____________                                                    
                                                         /        2                                                        
                                                        /      sin (t)                                                     
                                                       /   1 - -------                                                     
                                                      /           2                                                        
                                                    \/         cos (t)
6sin⁡4(t)cos⁡4(t)+8sin⁡2(t)cos⁡2(t)+2+4(sin⁡2(t)cos⁡2(t)+1)2sin⁡2(t)(−sin⁡2(t)cos⁡2(t)+1)cos⁡2(t)+(sin⁡2(t)cos⁡2(t)+1)(3sin⁡4(t)cos⁡4(t)+4sin⁡2(t)cos⁡2(t)+1)−sin⁡2(t)cos⁡2(t)+1+3(sin⁡2(t)cos⁡2(t)+1)3sin⁡2(t)(−sin⁡2(t)cos⁡2(t)+1)2cos⁡2(t)−sin⁡2(t)cos⁡2(t)+1\frac{\frac{6 \sin^{4}{\left(t \right)}}{\cos^{4}{\left(t \right)}} + \frac{8 \sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 2 + \frac{4 \left(\frac{\sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1\right)^{2} \sin^{2}{\left(t \right)}}{\left(- \frac{\sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1\right) \cos^{2}{\left(t \right)}} + \frac{\left(\frac{\sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1\right) \left(\frac{3 \sin^{4}{\left(t \right)}}{\cos^{4}{\left(t \right)}} + \frac{4 \sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1\right)}{- \frac{\sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1} + \frac{3 \left(\frac{\sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1\right)^{3} \sin^{2}{\left(t \right)}}{\left(- \frac{\sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1\right)^{2} \cos^{2}{\left(t \right)}}}{\sqrt{- \frac{\sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1}}
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Gráfico
Derivada de asin(sin(t)/cos(t))
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