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y(x)=-7x(arctg4x)10sin(7x)
Derivada de la función/ arctg/ ctg4x/ sin(7x)/ y(x)=-7x(arctg4x)10sin(7x)

Derivada de y(x)=-7x(arctg4x)10sin(7x)

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

Ha introducido [src] 
-7*x*atan(4*x)*10*sin(7*x)
10⋅−7xatan⁡(4x)sin⁡(7x)10 \cdot - 7 x \operatorname{atan}{\left(4 x \right)} \sin{\left(7 x \right)} 
(((-7*x)*atan(4*x))*10)*sin(7*x)
Gráfica
02468-8-6-4-2-1010-2000020000
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Primera derivada [src] 
/                  280*x  \                                    
|-70*atan(4*x) - ---------|*sin(7*x) - 490*x*atan(4*x)*cos(7*x)
|                        2|                                    
\                1 + 16*x /
−490xcos⁡(7x)atan⁡(4x)+(−280x16x2+1−70atan⁡(4x))sin⁡(7x)- 490 x \cos{\left(7 x \right)} \operatorname{atan}{\left(4 x \right)} + \left(- \frac{280 x}{16 x^{2} + 1} - 70 \operatorname{atan}{\left(4 x \right)}\right) \sin{\left(7 x \right)}
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Segunda derivada [src] 
   /                                          /           2  \                                   \
   |                                          |       16*x   |                                   |
   |                                        8*|-1 + ---------|*sin(7*x)                          |
   |                                          |             2|                                   |
   |     /   4*x               \              \     1 + 16*x /                                   |
70*|- 14*|--------- + atan(4*x)|*cos(7*x) + --------------------------- + 49*x*atan(4*x)*sin(7*x)|
   |     |        2            |                             2                                   |
   \     \1 + 16*x             /                     1 + 16*x                                    /
70(49xsin⁡(7x)atan⁡(4x)−14(4x16x2+1+atan⁡(4x))cos⁡(7x)+8(16x216x2+1−1)sin⁡(7x)16x2+1)70 \left(49 x \sin{\left(7 x \right)} \operatorname{atan}{\left(4 x \right)} - 14 \left(\frac{4 x}{16 x^{2} + 1} + \operatorname{atan}{\left(4 x \right)}\right) \cos{\left(7 x \right)} + \frac{8 \left(\frac{16 x^{2}}{16 x^{2} + 1} - 1\right) \sin{\left(7 x \right)}}{16 x^{2} + 1}\right)
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Tercera derivada [src] 
   /                                           /           2  \                                             /           2  \         \
   |                                           |       16*x   |                                             |       16*x   |         |
   |                                       168*|-1 + ---------|*cos(7*x)                              512*x*|-1 + ---------|*sin(7*x)|
   |                                           |             2|                                             |             2|         |
   |    /   4*x               \                \     1 + 16*x /                                             \     1 + 16*x /         |
70*|147*|--------- + atan(4*x)|*sin(7*x) + ----------------------------- + 343*x*atan(4*x)*cos(7*x) - -------------------------------|
   |    |        2            |                              2                                                             2         |
   |    \1 + 16*x             /                      1 + 16*x                                                   /        2\          |
   \                                                                                                            \1 + 16*x /          /
70(343xcos⁡(7x)atan⁡(4x)−512x(16x216x2+1−1)sin⁡(7x)(16x2+1)2+147(4x16x2+1+atan⁡(4x))sin⁡(7x)+168(16x216x2+1−1)cos⁡(7x)16x2+1)70 \left(343 x \cos{\left(7 x \right)} \operatorname{atan}{\left(4 x \right)} - \frac{512 x \left(\frac{16 x^{2}}{16 x^{2} + 1} - 1\right) \sin{\left(7 x \right)}}{\left(16 x^{2} + 1\right)^{2}} + 147 \left(\frac{4 x}{16 x^{2} + 1} + \operatorname{atan}{\left(4 x \right)}\right) \sin{\left(7 x \right)} + \frac{168 \left(\frac{16 x^{2}}{16 x^{2} + 1} - 1\right) \cos{\left(7 x \right)}}{16 x^{2} + 1}\right)
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Gráfico
Derivada de y(x)=-7x(arctg4x)10sin(7x)
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