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y=1/(sin(4x))+arcctg(3x^5)
Derivada de la función/ sin(4x)/ y=1/(sin(4x))+arcctg(3x^5)

Derivada de y=1/(sin(4x))+arcctg(3x^5)

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

Gráfico:

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Solución

Ha introducido [src] 
   1           /   5\
-------- + acot\3*x /
sin(4*x)
$$\operatorname{acot}{\left(3 x^{5} \right)} + \frac{1}{\sin{\left(4 x \right)}}$$ 
1/sin(4*x) + acot(3*x^5)
Gráfica
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
        4               
    15*x      4*cos(4*x)
- --------- - ----------
         10      2      
  1 + 9*x     sin (4*x)
$$- \frac{15 x^{4}}{9 x^{10} + 1} - \frac{4 \cos{\left(4 x \right)}}{\sin^{2}{\left(4 x \right)}}$$
Simplificar
Segunda derivada [src] 
  /                 3           2               13   \
  |   8         30*x      16*cos (4*x)     675*x     |
2*|-------- - --------- + ------------ + ------------|
  |sin(4*x)          10       3                     2|
  |           1 + 9*x      sin (4*x)     /       10\ |
  \                                      \1 + 9*x  / /
$$2 \left(\frac{675 x^{13}}{\left(9 x^{10} + 1\right)^{2}} - \frac{30 x^{3}}{9 x^{10} + 1} + \frac{8}{\sin{\left(4 x \right)}} + \frac{16 \cos^{2}{\left(4 x \right)}}{\sin^{3}{\left(4 x \right)}}\right)$$
Simplificar
Tercera derivada [src] 
  /           22           3                             2             12  \
  |   121500*x      192*cos (4*x)   160*cos(4*x)     90*x       11475*x    |
2*|- ------------ - ------------- - ------------ - --------- + ------------|
  |             3        4              2                 10              2|
  |  /       10\      sin (4*x)      sin (4*x)     1 + 9*x     /       10\ |
  \  \1 + 9*x  /                                               \1 + 9*x  / /
$$2 \left(- \frac{121500 x^{22}}{\left(9 x^{10} + 1\right)^{3}} + \frac{11475 x^{12}}{\left(9 x^{10} + 1\right)^{2}} - \frac{90 x^{2}}{9 x^{10} + 1} - \frac{160 \cos{\left(4 x \right)}}{\sin^{2}{\left(4 x \right)}} - \frac{192 \cos^{3}{\left(4 x \right)}}{\sin^{4}{\left(4 x \right)}}\right)$$
Simplificar
Gráfico
Derivada de y=1/(sin(4x))+arcctg(3x^5)
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