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Derivada de la función/ y=sin^7*x^7*((x^2+2x+4)/x^2-3)

Derivada de y=sin^7*x^7*((x^2+2x+4)/x^2-3)

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

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Solución

Ha introducido [src] 
             / 2              \
   823543    |x  + 2*x + 4    |
sin      (x)*|------------ - 3|
             |      2         |
             \     x          /
(−3+(x2+2x)+4x2)sin⁡823543(x)\left(-3 + \frac{\left(x^{2} + 2 x\right) + 4}{x^{2}}\right) \sin^{823543}{\left(x \right)} 
sin(x)^823543*((x^2 + 2*x + 4)/x^2 - 3)
Primera derivada [src] 
             /            / 2          \\                       / 2              \       
   823543    |2 + 2*x   2*\x  + 2*x + 4/|             823542    |x  + 2*x + 4    |       
sin      (x)*|------- - ----------------| + 823543*sin      (x)*|------------ - 3|*cos(x)
             |    2             3       |                       |      2         |       
             \   x             x        /                       \     x          /
823543(−3+(x2+2x)+4x2)sin⁡823542(x)cos⁡(x)+(2x+2x2−2((x2+2x)+4)x3)sin⁡823543(x)823543 \left(-3 + \frac{\left(x^{2} + 2 x\right) + 4}{x^{2}}\right) \sin^{823542}{\left(x \right)} \cos{\left(x \right)} + \left(\frac{2 x + 2}{x^{2}} - \frac{2 \left(\left(x^{2} + 2 x\right) + 4\right)}{x^{3}}\right) \sin^{823543}{\left(x \right)}
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Segunda derivada [src] 
             /                                                                 /                  /     2      \\                                               \
             |                                                            2    |    4*(1 + x)   3*\4 + x  + 2*x/|           /             2      \              |
             |                                                       2*sin (x)*|1 - --------- + ----------------|           |        4 + x  + 2*x|              |
             |       /         2      \                                        |        x               2       |   3294172*|1 + x - ------------|*cos(x)*sin(x)|
   823541    |       |    4 + x  + 2*x| /   2                2   \             \                       x        /           \             x      /              |
sin      (x)*|823543*|3 - ------------|*\sin (x) - 823542*cos (x)/ + -------------------------------------------- + --------------------------------------------|
             |       |          2     |                                                    2                                              2                     |
             \       \         x      /                                                   x                                              x                      /
(823543(3−x2+2x+4x2)(sin⁡2(x)−823542cos⁡2(x))+2(1−4(x+1)x+3(x2+2x+4)x2)sin⁡2(x)x2+3294172(x+1−x2+2x+4x)sin⁡(x)cos⁡(x)x2)sin⁡823541(x)\left(823543 \left(3 - \frac{x^{2} + 2 x + 4}{x^{2}}\right) \left(\sin^{2}{\left(x \right)} - 823542 \cos^{2}{\left(x \right)}\right) + \frac{2 \left(1 - \frac{4 \left(x + 1\right)}{x} + \frac{3 \left(x^{2} + 2 x + 4\right)}{x^{2}}\right) \sin^{2}{\left(x \right)}}{x^{2}} + \frac{3294172 \left(x + 1 - \frac{x^{2} + 2 x + 4}{x}\right) \sin{\left(x \right)} \cos{\left(x \right)}}{x^{2}}\right) \sin^{823541}{\left(x \right)}
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Tercera derivada [src] 
             /             /                  /     2      \\                                                                                                                                                                    /                  /     2      \\       \
             |        3    |    3*(1 + x)   2*\4 + x  + 2*x/|                                                                                                                    /             2      \                     2    |    4*(1 + x)   3*\4 + x  + 2*x/|       |
             |  12*sin (x)*|1 - --------- + ----------------|                                                                                         /   2                2   \ |        4 + x  + 2*x|          4941258*sin (x)*|1 - --------- + ----------------|*cos(x)|
             |             |        x               2       |          /         2      \                                                     4941258*\sin (x) - 823542*cos (x)/*|1 + x - ------------|*sin(x)                   |        x               2       |       |
   823540    |             \                       x        /          |    4 + x  + 2*x| /                  2                 2   \                                             \             x      /                          \                       x        /       |
sin      (x)*|- --------------------------------------------- + 823543*|3 - ------------|*\- 678220602222*cos (x) + 2470627*sin (x)/*cos(x) - ---------------------------------------------------------------- + ---------------------------------------------------------|
             |                         3                               |          2     |                                                                                     2                                                               2                           |
             \                        x                                \         x      /                                                                                    x                                                               x                            /
(823543(3−x2+2x+4x2)(2470627sin⁡2(x)−678220602222cos⁡2(x))cos⁡(x)−4941258(sin⁡2(x)−823542cos⁡2(x))(x+1−x2+2x+4x)sin⁡(x)x2+4941258(1−4(x+1)x+3(x2+2x+4)x2)sin⁡2(x)cos⁡(x)x2−12(1−3(x+1)x+2(x2+2x+4)x2)sin⁡3(x)x3)sin⁡823540(x)\left(823543 \left(3 - \frac{x^{2} + 2 x + 4}{x^{2}}\right) \left(2470627 \sin^{2}{\left(x \right)} - 678220602222 \cos^{2}{\left(x \right)}\right) \cos{\left(x \right)} - \frac{4941258 \left(\sin^{2}{\left(x \right)} - 823542 \cos^{2}{\left(x \right)}\right) \left(x + 1 - \frac{x^{2} + 2 x + 4}{x}\right) \sin{\left(x \right)}}{x^{2}} + \frac{4941258 \left(1 - \frac{4 \left(x + 1\right)}{x} + \frac{3 \left(x^{2} + 2 x + 4\right)}{x^{2}}\right) \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{x^{2}} - \frac{12 \left(1 - \frac{3 \left(x + 1\right)}{x} + \frac{2 \left(x^{2} + 2 x + 4\right)}{x^{2}}\right) \sin^{3}{\left(x \right)}}{x^{3}}\right) \sin^{823540}{\left(x \right)}
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