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y=arcsin(sin^4x-cos^4x)
Derivada de la función/ sin^4/ arcsin/ cos^4x/ y=arcsin(sin^4x-cos^4x)

Derivada de y=arcsin(sin^4x-cos^4x)

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

Ha introducido [src] 
    /   4         4   \
asin\sin (x) - cos (x)/
asin⁡(sin⁡4(x)−cos⁡4(x))\operatorname{asin}{\left(\sin^{4}{\left(x \right)} - \cos^{4}{\left(x \right)} \right)} 
asin(sin(x)^4 - cos(x)^4)
Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
     3                  3          
4*cos (x)*sin(x) + 4*sin (x)*cos(x)
-----------------------------------
       __________________________  
      /                        2   
     /      /   4         4   \    
   \/   1 - \sin (x) - cos (x)/
4sin⁡3(x)cos⁡(x)+4sin⁡(x)cos⁡3(x)1−(sin⁡4(x)−cos⁡4(x))2\frac{4 \sin^{3}{\left(x \right)} \cos{\left(x \right)} + 4 \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{\sqrt{1 - \left(\sin^{4}{\left(x \right)} - \cos^{4}{\left(x \right)}\right)^{2}}}
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Segunda derivada [src] 
  /                          2                \                    
  |       /   2         2   \     2       2   |                    
  |     4*\cos (x) + sin (x)/ *cos (x)*sin (x)| /   4         4   \
4*|-1 + --------------------------------------|*\sin (x) - cos (x)/
  |                                   2       |                    
  |                /   4         4   \        |                    
  \            1 - \sin (x) - cos (x)/        /                    
-------------------------------------------------------------------
                       __________________________                  
                      /                        2                   
                     /      /   4         4   \                    
                   \/   1 - \sin (x) - cos (x)/
4(−1+4(sin⁡2(x)+cos⁡2(x))2sin⁡2(x)cos⁡2(x)1−(sin⁡4(x)−cos⁡4(x))2)(sin⁡4(x)−cos⁡4(x))1−(sin⁡4(x)−cos⁡4(x))2\frac{4 \left(-1 + \frac{4 \left(\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right)^{2} \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{1 - \left(\sin^{4}{\left(x \right)} - \cos^{4}{\left(x \right)}\right)^{2}}\right) \left(\sin^{4}{\left(x \right)} - \cos^{4}{\left(x \right)}\right)}{\sqrt{1 - \left(\sin^{4}{\left(x \right)} - \cos^{4}{\left(x \right)}\right)^{2}}}
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Tercera derivada [src] 
                       /                           2                         2                                         2                    2                \              
                       |        /   4         4   \       /   2         2   \     2       2         /   2         2   \  /   4         4   \     2       2   |              
   /   2         2   \ |      3*\sin (x) - cos (x)/     4*\cos (x) + sin (x)/ *cos (x)*sin (x)   12*\cos (x) + sin (x)/ *\sin (x) - cos (x)/ *cos (x)*sin (x)|              
16*\cos (x) + sin (x)/*|-1 - ------------------------ + -------------------------------------- + ------------------------------------------------------------|*cos(x)*sin(x)
                       |                            2                                 2                                                    2                 |              
                       |         /   4         4   \               /   4         4   \                           /                       2\                  |              
                       |     1 - \sin (x) - cos (x)/           1 - \sin (x) - cos (x)/                           |    /   4         4   \ |                  |              
                       \                                                                                         \1 - \sin (x) - cos (x)/ /                  /              
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                           __________________________                                                                       
                                                                          /                        2                                                                        
                                                                         /      /   4         4   \                                                                         
                                                                       \/   1 - \sin (x) - cos (x)/
16(sin⁡2(x)+cos⁡2(x))(−1+4(sin⁡2(x)+cos⁡2(x))2sin⁡2(x)cos⁡2(x)1−(sin⁡4(x)−cos⁡4(x))2−3(sin⁡4(x)−cos⁡4(x))21−(sin⁡4(x)−cos⁡4(x))2+12(sin⁡2(x)+cos⁡2(x))2(sin⁡4(x)−cos⁡4(x))2sin⁡2(x)cos⁡2(x)(1−(sin⁡4(x)−cos⁡4(x))2)2)sin⁡(x)cos⁡(x)1−(sin⁡4(x)−cos⁡4(x))2\frac{16 \left(\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right) \left(-1 + \frac{4 \left(\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right)^{2} \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{1 - \left(\sin^{4}{\left(x \right)} - \cos^{4}{\left(x \right)}\right)^{2}} - \frac{3 \left(\sin^{4}{\left(x \right)} - \cos^{4}{\left(x \right)}\right)^{2}}{1 - \left(\sin^{4}{\left(x \right)} - \cos^{4}{\left(x \right)}\right)^{2}} + \frac{12 \left(\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right)^{2} \left(\sin^{4}{\left(x \right)} - \cos^{4}{\left(x \right)}\right)^{2} \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{\left(1 - \left(\sin^{4}{\left(x \right)} - \cos^{4}{\left(x \right)}\right)^{2}\right)^{2}}\right) \sin{\left(x \right)} \cos{\left(x \right)}}{\sqrt{1 - \left(\sin^{4}{\left(x \right)} - \cos^{4}{\left(x \right)}\right)^{2}}}
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Gráfico
Derivada de y=arcsin(sin^4x-cos^4x)
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