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Derivada de la función/ (4+3x^3)/xsqrt^3((2+x^3)^2)

Derivada de (4+3x^3)/xsqrt^3((2+x^3)^2)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
                        3
             ___________ 
       3    /         2  
4 + 3*x    /  /     3\   
--------*\/   \2 + x /   
   x
3x3+4x((x3+2)2)3\frac{3 x^{3} + 4}{x} \left(\sqrt{\left(x^{3} + 2\right)^{2}}\right)^{3} 
((4 + 3*x^3)/x)*(sqrt((2 + x^3)^2))^3
Primera derivada [src] 
        2          /             3\                                   
/     3\  |     3| |      4 + 3*x |       /     3\ /       3\ |     3|
\2 + x / *|2 + x |*|9*x - --------| + 9*x*\2 + x /*\4 + 3*x /*|2 + x |
                   |          2   |                                   
                   \         x    /
9x(x3+2)(3x3+4)∣x3+2∣+(x3+2)2∣x3+2∣(9x−3x3+4x2)9 x \left(x^{3} + 2\right) \left(3 x^{3} + 4\right) \left|{x^{3} + 2}\right| + \left(x^{3} + 2\right)^{2} \left|{x^{3} + 2}\right| \left(9 x - \frac{3 x^{3} + 4}{x^{2}}\right)
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Segunda derivada [src] 
                                                                                                             2                                                               
                                                                                                     /     3\  /       3\ |     3|                  /             3\         
  /       3\ /     3 |     3|     /     3\ |     3|      3 /  |     3|   /     3\     /     3\\\   2*\2 + x / *\4 + 3*x /*|2 + x |       2 /     3\ |      4 + 3*x | |     3|
9*\4 + 3*x /*\- 3*x *|2 + x | + 2*\2 + x /*|2 + x | + 3*x *\2*|2 + x | + \2 + x /*sign\2 + x /// + ------------------------------- + 18*x *\2 + x /*|9*x - --------|*|2 + x |
                                                                                                                   3                                |          2   |         
                                                                                                                  x                                 \         x    /
18x2(9x−3x3+4x2)(x3+2)∣x3+2∣+9(3x3+4)(3x3((x3+2)sign⁡(x3+2)+2∣x3+2∣)−3x3∣x3+2∣+2(x3+2)∣x3+2∣)+2(x3+2)2(3x3+4)∣x3+2∣x318 x^{2} \left(9 x - \frac{3 x^{3} + 4}{x^{2}}\right) \left(x^{3} + 2\right) \left|{x^{3} + 2}\right| + 9 \left(3 x^{3} + 4\right) \left(3 x^{3} \left(\left(x^{3} + 2\right) \operatorname{sign}{\left(x^{3} + 2 \right)} + 2 \left|{x^{3} + 2}\right|\right) - 3 x^{3} \left|{x^{3} + 2}\right| + 2 \left(x^{3} + 2\right) \left|{x^{3} + 2}\right|\right) + \frac{2 \left(x^{3} + 2\right)^{2} \left(3 x^{3} + 4\right) \left|{x^{3} + 2}\right|}{x^{3}}
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Tercera derivada [src] 
  /             /                                                                                                                                                         /        2                                                                   2                                                \                             \                                                                                                                                                                                   \
  |             |                                                                                                           6 /  |     3|   /     3\     /     3\\      3 |/     3\      /     3\     /     3\ |     3|      3 |     3|      3 /     3\            /     3\      3 /     3\     /     3\|                             |                                                                                                                        2 /           3\                                           |
  |  /       3\ |     6     /     3\      3 |     3|     /     3\ |     3|      3 /  |     3|   /     3\     /     3\\   9*x *\2*|2 + x | + \2 + x /*sign\2 + x //   6*x *\\2 + x / *sign\2 + x / + 2*\2 + x /*|2 + x | + 3*x *|2 + x | + 3*x *\2 + x / *DiracDelta\2 + x / + 6*x *\2 + x /*sign\2 + x //      3 /     3\     /     3\|                                                                                                                /     3\  |    4 + 3*x | |     3|                                  |
  |3*\4 + 3*x /*|- 9*x *sign\2 + x / - 6*x *|2 + x | + 2*\2 + x /*|2 + x | + 6*x *\2*|2 + x | + \2 + x /*sign\2 + x // - ----------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------ + 6*x *\2 + x /*sign\2 + x /|                                                                                                              2*\2 + x / *|3 - --------|*|2 + x |                                  |
  |             |                                                                                                                               3                                                                                        3                                                                                            |       /             3\                                                                                                   |        3   |               /     3\ /       3\ |     3||
  |             \                                                                                                                          2 + x                                                                                    2 + x                                                                                             /       |      4 + 3*x | /     3 |     3|     /     3\ |     3|      3 /  |     3|   /     3\     /     3\\\               \       x    /            18*\2 + x /*\4 + 3*x /*|2 + x ||
3*|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + 9*x*|9*x - --------|*\- 3*x *|2 + x | + 2*\2 + x /*|2 + x | + 3*x *\2*|2 + x | + \2 + x /*sign\2 + x /// + ----------------------------------- + -------------------------------|
  |                                                                                                                                                                 x                                                                                                                                                                         |          2   |                                                                                                        x                                   x               |
  \                                                                                                                                                                                                                                                                                                                                           \         x    /                                                                                                                                                            /
3(9x(9x−3x3+4x2)(3x3((x3+2)sign⁡(x3+2)+2∣x3+2∣)−3x3∣x3+2∣+2(x3+2)∣x3+2∣)+2(3−3x3+4x3)(x3+2)2∣x3+2∣x+18(x3+2)(3x3+4)∣x3+2∣x+3(3x3+4)(−9x6sign⁡(x3+2)−9x6((x3+2)sign⁡(x3+2)+2∣x3+2∣)x3+2+6x3(x3+2)sign⁡(x3+2)+6x3((x3+2)sign⁡(x3+2)+2∣x3+2∣)−6x3∣x3+2∣+6x3(3x3(x3+2)2δ(x3+2)+6x3(x3+2)sign⁡(x3+2)+3x3∣x3+2∣+(x3+2)2sign⁡(x3+2)+2(x3+2)∣x3+2∣)x3+2+2(x3+2)∣x3+2∣)x)3 \left(9 x \left(9 x - \frac{3 x^{3} + 4}{x^{2}}\right) \left(3 x^{3} \left(\left(x^{3} + 2\right) \operatorname{sign}{\left(x^{3} + 2 \right)} + 2 \left|{x^{3} + 2}\right|\right) - 3 x^{3} \left|{x^{3} + 2}\right| + 2 \left(x^{3} + 2\right) \left|{x^{3} + 2}\right|\right) + \frac{2 \left(3 - \frac{3 x^{3} + 4}{x^{3}}\right) \left(x^{3} + 2\right)^{2} \left|{x^{3} + 2}\right|}{x} + \frac{18 \left(x^{3} + 2\right) \left(3 x^{3} + 4\right) \left|{x^{3} + 2}\right|}{x} + \frac{3 \left(3 x^{3} + 4\right) \left(- 9 x^{6} \operatorname{sign}{\left(x^{3} + 2 \right)} - \frac{9 x^{6} \left(\left(x^{3} + 2\right) \operatorname{sign}{\left(x^{3} + 2 \right)} + 2 \left|{x^{3} + 2}\right|\right)}{x^{3} + 2} + 6 x^{3} \left(x^{3} + 2\right) \operatorname{sign}{\left(x^{3} + 2 \right)} + 6 x^{3} \left(\left(x^{3} + 2\right) \operatorname{sign}{\left(x^{3} + 2 \right)} + 2 \left|{x^{3} + 2}\right|\right) - 6 x^{3} \left|{x^{3} + 2}\right| + \frac{6 x^{3} \left(3 x^{3} \left(x^{3} + 2\right)^{2} \delta\left(x^{3} + 2\right) + 6 x^{3} \left(x^{3} + 2\right) \operatorname{sign}{\left(x^{3} + 2 \right)} + 3 x^{3} \left|{x^{3} + 2}\right| + \left(x^{3} + 2\right)^{2} \operatorname{sign}{\left(x^{3} + 2 \right)} + 2 \left(x^{3} + 2\right) \left|{x^{3} + 2}\right|\right)}{x^{3} + 2} + 2 \left(x^{3} + 2\right) \left|{x^{3} + 2}\right|\right)}{x}\right)
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