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y=(arcsin4x)/((cos^5)2x)
Derivada de la función/ sin4x/ arcsin/ y=(arcsin4x)/((cos^5)2x)

Derivada de y=(arcsin4x)/((cos^5)2x)

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src] 
 asin(4*x) 
-----------
   5       
cos (x)*2*x
asin⁡(4x)x2cos⁡5(x)\frac{\operatorname{asin}{\left(4 x \right)}}{x 2 \cos^{5}{\left(x \right)}} 
asin(4*x)/(((cos(x)^5*2)*x))
Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
       1                                                      
4*-----------                                                 
         5       /     5                4          \          
  2*x*cos (x)    \- cos (x)*2 + 10*x*cos (x)*sin(x)/*asin(4*x)
-------------- + ---------------------------------------------
   ___________                      2    10                   
  /         2                    4*x *cos  (x)                
\/  1 - 16*x
412xcos⁡5(x)1−16x2+(10xsin⁡(x)cos⁡4(x)−2cos⁡5(x))asin⁡(4x)4x2cos⁡10(x)\frac{4 \frac{1}{2 x \cos^{5}{\left(x \right)}}}{\sqrt{1 - 16 x^{2}}} + \frac{\left(10 x \sin{\left(x \right)} \cos^{4}{\left(x \right)} - 2 \cos^{5}{\left(x \right)}\right) \operatorname{asin}{\left(4 x \right)}}{4 x^{2} \cos^{10}{\left(x \right)}}
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Segunda derivada [src] 
                 /                                                                   /     2             2                     \                                  \                                     
                 |/  1   5*sin(x)\                          -cos(x) + 5*x*sin(x)   5*\x*cos (x) - 4*x*sin (x) + 2*cos(x)*sin(x)/   5*(-cos(x) + 5*x*sin(x))*sin(x)|                                     
                 ||- - + --------|*(-cos(x) + 5*x*sin(x)) - -------------------- + --------------------------------------------- + -------------------------------|*asin(4*x)                           
      32         \\  x    cos(x) /                                   x                                 cos(x)                                   cos(x)            /             4*(-cos(x) + 5*x*sin(x))
-------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------ + ------------------------
           3/2                                                                              2                                                                                         ___________       
/        2\                                                                              2*x *cos(x)                                                                             2   /         2        
\1 - 16*x /                                                                                                                                                                     x *\/  1 - 16*x  *cos(x)
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                   5                                                                                                    
                                                                                                cos (x)
32(1−16x2)32+((5xsin⁡(x)−cos⁡(x))(5sin⁡(x)cos⁡(x)−1x)+5(5xsin⁡(x)−cos⁡(x))sin⁡(x)cos⁡(x)+5(−4xsin⁡2(x)+xcos⁡2(x)+2sin⁡(x)cos⁡(x))cos⁡(x)−5xsin⁡(x)−cos⁡(x)x)asin⁡(4x)2x2cos⁡(x)+4(5xsin⁡(x)−cos⁡(x))x21−16x2cos⁡(x)cos⁡5(x)\frac{\frac{32}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}} + \frac{\left(\left(5 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \left(\frac{5 \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{1}{x}\right) + \frac{5 \left(5 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{5 \left(- 4 x \sin^{2}{\left(x \right)} + x \cos^{2}{\left(x \right)} + 2 \sin{\left(x \right)} \cos{\left(x \right)}\right)}{\cos{\left(x \right)}} - \frac{5 x \sin{\left(x \right)} - \cos{\left(x \right)}}{x}\right) \operatorname{asin}{\left(4 x \right)}}{2 x^{2} \cos{\left(x \right)}} + \frac{4 \left(5 x \sin{\left(x \right)} - \cos{\left(x \right)}\right)}{x^{2} \sqrt{1 - 16 x^{2}} \cos{\left(x \right)}}}{\cos^{5}{\left(x \right)}}
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Tercera derivada [src] 
                                                     /                                                                                                                                                                                         /  1   5*sin(x)\                                                                             /  1   5*sin(x)\ /     2             2                     \                                                                                                                                    /  1   5*sin(x)\                              \                                                                                                                                                                 
     /           2   \                               |                                   /               2               \                                /     3            2                     3              2          \                 |- - + --------|*(-cos(x) + 5*x*sin(x))      /     2             2                     \   5*|- - + --------|*\x*cos (x) - 4*x*sin (x) + 2*cos(x)*sin(x)/         2                                /     2             2                     \                                             5*|- - + --------|*(-cos(x) + 5*x*sin(x))*sin(x)|                                                                                                                                                                 
     |       48*x    |                               |                                   |    2    30*sin (x)   10*sin(x)|   3*(-cos(x) + 5*x*sin(x))   5*\3*cos (x) - 12*sin (x)*cos(x) + 12*x*sin (x) - 13*x*cos (x)*sin(x)/                 \  x    cos(x) /                          15*\x*cos (x) - 4*x*sin (x) + 2*cos(x)*sin(x)/     \  x    cos(x) /                                               55*sin (x)*(-cos(x) + 5*x*sin(x))   75*\x*cos (x) - 4*x*sin (x) + 2*cos(x)*sin(x)/*sin(x)   20*(-cos(x) + 5*x*sin(x))*sin(x)     \  x    cos(x) /                              |               /                                                                   /     2             2                     \                                  \
  32*|-1 + ----------|                               |-5*cos(x) + (-cos(x) + 5*x*sin(x))*|5 + -- + ---------- - ---------| + ------------------------ + ---------------------------------------------------------------------- + 25*x*sin(x) - --------------------------------------- - ---------------------------------------------- + -------------------------------------------------------------- + --------------------------------- + ----------------------------------------------------- - -------------------------------- + ------------------------------------------------|*asin(4*x)     |/  1   5*sin(x)\                          -cos(x) + 5*x*sin(x)   5*\x*cos (x) - 4*x*sin (x) + 2*cos(x)*sin(x)/   5*(-cos(x) + 5*x*sin(x))*sin(x)|
     |              2|                               |                                   |     2       2         x*cos(x)|               2                                                2                                                                       x                                         x*cos(x)                                                  cos(x)                                               2                                             2                                         x*cos(x)                                    cos(x)                     |             6*||- - + --------|*(-cos(x) + 5*x*sin(x)) - -------------------- + --------------------------------------------- + -------------------------------|
     \     -1 + 16*x /   96*(-cos(x) + 5*x*sin(x))   \                                   \    x     cos (x)              /              x                                              cos (x)                                                                                                                                                                                                                          cos (x)                                       cos (x)                                                                                                             /               \\  x    cos(x) /                                   x                                 cos(x)                                   cos(x)            /
- -------------------- + ------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ----------------------------------------------------------------------------------------------------------------------------------------------------
                3/2                   3/2                                                                                                                                                                                                                                                                               2*x*cos(x)                                                                                                                                                                                                                                                                                                                                         ___________                                                                      
     /        2\           /        2\                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    /         2                                                                       
     \1 - 16*x /           \1 - 16*x /   *cos(x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      x*\/  1 - 16*x  *cos(x)                                                               
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                                                                                                                                              5                                                                                                                                                                                                                                                                                                                                                                             
                                                                                                                                                                                                                                                                                                                                                                         x*cos (x)
96(5xsin⁡(x)−cos⁡(x))(1−16x2)32cos⁡(x)−32(48x216x2−1−1)(1−16x2)32+(25xsin⁡(x)+5(5xsin⁡(x)−cos⁡(x))(5sin⁡(x)cos⁡(x)−1x)sin⁡(x)cos⁡(x)+(5xsin⁡(x)−cos⁡(x))(30sin⁡2(x)cos⁡2(x)+5−10sin⁡(x)xcos⁡(x)+2x2)+55(5xsin⁡(x)−cos⁡(x))sin⁡2(x)cos⁡2(x)+5(5sin⁡(x)cos⁡(x)−1x)(−4xsin⁡2(x)+xcos⁡2(x)+2sin⁡(x)cos⁡(x))cos⁡(x)+75(−4xsin⁡2(x)+xcos⁡2(x)+2sin⁡(x)cos⁡(x))sin⁡(x)cos⁡2(x)+5(12xsin⁡3(x)−13xsin⁡(x)cos⁡2(x)−12sin⁡2(x)cos⁡(x)+3cos⁡3(x))cos⁡2(x)−5cos⁡(x)−(5xsin⁡(x)−cos⁡(x))(5sin⁡(x)cos⁡(x)−1x)x−20(5xsin⁡(x)−cos⁡(x))sin⁡(x)xcos⁡(x)−15(−4xsin⁡2(x)+xcos⁡2(x)+2sin⁡(x)cos⁡(x))xcos⁡(x)+3(5xsin⁡(x)−cos⁡(x))x2)asin⁡(4x)2xcos⁡(x)+6((5xsin⁡(x)−cos⁡(x))(5sin⁡(x)cos⁡(x)−1x)+5(5xsin⁡(x)−cos⁡(x))sin⁡(x)cos⁡(x)+5(−4xsin⁡2(x)+xcos⁡2(x)+2sin⁡(x)cos⁡(x))cos⁡(x)−5xsin⁡(x)−cos⁡(x)x)x1−16x2cos⁡(x)xcos⁡5(x)\frac{\frac{96 \left(5 x \sin{\left(x \right)} - \cos{\left(x \right)}\right)}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}} \cos{\left(x \right)}} - \frac{32 \left(\frac{48 x^{2}}{16 x^{2} - 1} - 1\right)}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}} + \frac{\left(25 x \sin{\left(x \right)} + \frac{5 \left(5 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \left(\frac{5 \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{1}{x}\right) \sin{\left(x \right)}}{\cos{\left(x \right)}} + \left(5 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \left(\frac{30 \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 5 - \frac{10 \sin{\left(x \right)}}{x \cos{\left(x \right)}} + \frac{2}{x^{2}}\right) + \frac{55 \left(5 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + \frac{5 \left(\frac{5 \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{1}{x}\right) \left(- 4 x \sin^{2}{\left(x \right)} + x \cos^{2}{\left(x \right)} + 2 \sin{\left(x \right)} \cos{\left(x \right)}\right)}{\cos{\left(x \right)}} + \frac{75 \left(- 4 x \sin^{2}{\left(x \right)} + x \cos^{2}{\left(x \right)} + 2 \sin{\left(x \right)} \cos{\left(x \right)}\right) \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}} + \frac{5 \left(12 x \sin^{3}{\left(x \right)} - 13 x \sin{\left(x \right)} \cos^{2}{\left(x \right)} - 12 \sin^{2}{\left(x \right)} \cos{\left(x \right)} + 3 \cos^{3}{\left(x \right)}\right)}{\cos^{2}{\left(x \right)}} - 5 \cos{\left(x \right)} - \frac{\left(5 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \left(\frac{5 \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{1}{x}\right)}{x} - \frac{20 \left(5 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \sin{\left(x \right)}}{x \cos{\left(x \right)}} - \frac{15 \left(- 4 x \sin^{2}{\left(x \right)} + x \cos^{2}{\left(x \right)} + 2 \sin{\left(x \right)} \cos{\left(x \right)}\right)}{x \cos{\left(x \right)}} + \frac{3 \left(5 x \sin{\left(x \right)} - \cos{\left(x \right)}\right)}{x^{2}}\right) \operatorname{asin}{\left(4 x \right)}}{2 x \cos{\left(x \right)}} + \frac{6 \left(\left(5 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \left(\frac{5 \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{1}{x}\right) + \frac{5 \left(5 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{5 \left(- 4 x \sin^{2}{\left(x \right)} + x \cos^{2}{\left(x \right)} + 2 \sin{\left(x \right)} \cos{\left(x \right)}\right)}{\cos{\left(x \right)}} - \frac{5 x \sin{\left(x \right)} - \cos{\left(x \right)}}{x}\right)}{x \sqrt{1 - 16 x^{2}} \cos{\left(x \right)}}}{x \cos^{5}{\left(x \right)}}
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Gráfico
Derivada de y=(arcsin4x)/((cos^5)2x)
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