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y=arctg5x*sin4x
Derivada de la función/ x*sin/ sin4x/ arctg/ ctg5x/ y=arctg5x*sin4x

Derivada de y=arctg5x*sin4x

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

Ha introducido [src] 
atan(5*x)*sin(4*x)
sin⁡(4x)atan⁡(5x)\sin{\left(4 x \right)} \operatorname{atan}{\left(5 x \right)} 
atan(5*x)*sin(4*x)
Gráfica
02468-8-6-4-2-1010-1010
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                       5*sin(4*x)
4*atan(5*x)*cos(4*x) + ----------
                               2 
                       1 + 25*x
4cos⁡(4x)atan⁡(5x)+5sin⁡(4x)25x2+14 \cos{\left(4 x \right)} \operatorname{atan}{\left(5 x \right)} + \frac{5 \sin{\left(4 x \right)}}{25 x^{2} + 1}
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Segunda derivada [src] 
  /                        20*cos(4*x)   125*x*sin(4*x)\
2*|-8*atan(5*x)*sin(4*x) + ----------- - --------------|
  |                                 2                2 |
  |                         1 + 25*x      /        2\  |
  \                                       \1 + 25*x /  /
2(−125xsin⁡(4x)(25x2+1)2−8sin⁡(4x)atan⁡(5x)+20cos⁡(4x)25x2+1)2 \left(- \frac{125 x \sin{\left(4 x \right)}}{\left(25 x^{2} + 1\right)^{2}} - 8 \sin{\left(4 x \right)} \operatorname{atan}{\left(5 x \right)} + \frac{20 \cos{\left(4 x \right)}}{25 x^{2} + 1}\right)
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Tercera derivada [src] 
  /                                                               /            2 \         \
  |                                                               |       100*x  |         |
  |                                                           125*|-1 + ---------|*sin(4*x)|
  |                                                               |             2|         |
  |  120*sin(4*x)                           1500*x*cos(4*x)       \     1 + 25*x /         |
2*|- ------------ - 32*atan(5*x)*cos(4*x) - --------------- + -----------------------------|
  |           2                                          2                        2        |
  |   1 + 25*x                                /        2\              /        2\         |
  \                                           \1 + 25*x /              \1 + 25*x /         /
2(−1500xcos⁡(4x)(25x2+1)2−32cos⁡(4x)atan⁡(5x)−120sin⁡(4x)25x2+1+125(100x225x2+1−1)sin⁡(4x)(25x2+1)2)2 \left(- \frac{1500 x \cos{\left(4 x \right)}}{\left(25 x^{2} + 1\right)^{2}} - 32 \cos{\left(4 x \right)} \operatorname{atan}{\left(5 x \right)} - \frac{120 \sin{\left(4 x \right)}}{25 x^{2} + 1} + \frac{125 \left(\frac{100 x^{2}}{25 x^{2} + 1} - 1\right) \sin{\left(4 x \right)}}{\left(25 x^{2} + 1\right)^{2}}\right)
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Gráfico
Derivada de y=arctg5x*sin4x
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