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y=arcctg^8lg(x^3+5x^2+2x)
Derivada de la función/ x^2+2/ x^3+5x/ y=arcctg^8lg(x^3+5x^2+2x)

Derivada de y=arcctg^8lg(x^3+5x^2+2x)

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

Gráfico:

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Solución

Gráfica
02468-8-6-4-2-1010-500500
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Primera derivada [src] 
    8    /       2       \         7       / 3      2      \
acot (x)*\2 + 3*x  + 10*x/   8*acot (x)*log\x  + 5*x  + 2*x/
-------------------------- - -------------------------------
      3      2                                 2            
     x  + 5*x  + 2*x                      1 + x
−8log⁡(2x+(x3+5x2))acot⁡7(x)x2+1+(3x2+10x+2)acot⁡8(x)2x+(x3+5x2)- \frac{8 \log{\left(2 x + \left(x^{3} + 5 x^{2}\right) \right)} \operatorname{acot}^{7}{\left(x \right)}}{x^{2} + 1} + \frac{\left(3 x^{2} + 10 x + 2\right) \operatorname{acot}^{8}{\left(x \right)}}{2 x + \left(x^{3} + 5 x^{2}\right)}
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Segunda derivada [src] 
         /                                                     /                            2\                               \
         |                                                     |           /       2       \ |                               |
         |                                                2    |           \2 + 3*x  + 10*x/ |                               |
         |                                            acot (x)*|10 + 6*x - ------------------|                               |
         |                       /  /     2      \\            |              /     2      \ |      /       2       \        |
    6    |8*(7 + 2*x*acot(x))*log\x*\2 + x  + 5*x//            \            x*\2 + x  + 5*x/ /   16*\2 + 3*x  + 10*x/*acot(x)|
acot (x)*|----------------------------------------- + ---------------------------------------- - ----------------------------|
         |                        2                                 /     2      \                  /     2\ /     2      \  |
         |                /     2\                                x*\2 + x  + 5*x/                x*\1 + x /*\2 + x  + 5*x/  |
         \                \1 + x /                                                                                           /
(8(2xacot⁡(x)+7)log⁡(x(x2+5x+2))(x2+1)2+(6x+10−(3x2+10x+2)2x(x2+5x+2))acot⁡2(x)x(x2+5x+2)−16(3x2+10x+2)acot⁡(x)x(x2+1)(x2+5x+2))acot⁡6(x)\left(\frac{8 \left(2 x \operatorname{acot}{\left(x \right)} + 7\right) \log{\left(x \left(x^{2} + 5 x + 2\right) \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{\left(6 x + 10 - \frac{\left(3 x^{2} + 10 x + 2\right)^{2}}{x \left(x^{2} + 5 x + 2\right)}\right) \operatorname{acot}^{2}{\left(x \right)}}{x \left(x^{2} + 5 x + 2\right)} - \frac{16 \left(3 x^{2} + 10 x + 2\right) \operatorname{acot}{\left(x \right)}}{x \left(x^{2} + 1\right) \left(x^{2} + 5 x + 2\right)}\right) \operatorname{acot}^{6}{\left(x \right)}
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Tercera derivada [src] 
           /                                                                                          /                     3                                \                                                                                               \
           |                                                                                          |    /       2       \                /       2       \|               /                            2\                                                 |
           |    /                         2     2                  \                             3    |    \2 + 3*x  + 10*x/    3*(5 + 3*x)*\2 + 3*x  + 10*x/|               |           /       2       \ |                                                 |
           |    |      2        21     4*x *acot (x)   21*x*acot(x)|    /  /     2      \\   acot (x)*|3 + ------------------ - -----------------------------|          2    |           \2 + 3*x  + 10*x/ |                                                 |
           |  8*|- acot (x) + ------ + ------------- + ------------|*log\x*\2 + x  + 5*x//            |                     2            /     2      \      |   12*acot (x)*|10 + 6*x - ------------------|                                                 |
           |    |                  2            2              2   |                                  |     2 /     2      \           x*\2 + x  + 5*x/      |               |              /     2      \ |                        /       2       \        |
      5    |    \             1 + x        1 + x          1 + x    /                                  \    x *\2 + x  + 5*x/                                 /               \            x*\2 + x  + 5*x/ /   12*(7 + 2*x*acot(x))*\2 + 3*x  + 10*x/*acot(x)|
2*acot (x)*|- ---------------------------------------------------------------------------- + ----------------------------------------------------------------- - ------------------------------------------- + ----------------------------------------------|
           |                                           2                                                                /     2      \                                      /     2\ /     2      \                                2                         |
           |                                   /     2\                                                               x*\2 + x  + 5*x/                                    x*\1 + x /*\2 + x  + 5*x/                        /     2\  /     2      \          |
           \                                   \1 + x /                                                                                                                                                                  x*\1 + x / *\2 + x  + 5*x/          /
2(−8(4x2acot⁡2(x)x2+1+21xacot⁡(x)x2+1−acot⁡2(x)+21x2+1)log⁡(x(x2+5x+2))(x2+1)2+(3−3(3x+5)(3x2+10x+2)x(x2+5x+2)+(3x2+10x+2)3x2(x2+5x+2)2)acot⁡3(x)x(x2+5x+2)−12(6x+10−(3x2+10x+2)2x(x2+5x+2))acot⁡2(x)x(x2+1)(x2+5x+2)+12(2xacot⁡(x)+7)(3x2+10x+2)acot⁡(x)x(x2+1)2(x2+5x+2))acot⁡5(x)2 \left(- \frac{8 \left(\frac{4 x^{2} \operatorname{acot}^{2}{\left(x \right)}}{x^{2} + 1} + \frac{21 x \operatorname{acot}{\left(x \right)}}{x^{2} + 1} - \operatorname{acot}^{2}{\left(x \right)} + \frac{21}{x^{2} + 1}\right) \log{\left(x \left(x^{2} + 5 x + 2\right) \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{\left(3 - \frac{3 \left(3 x + 5\right) \left(3 x^{2} + 10 x + 2\right)}{x \left(x^{2} + 5 x + 2\right)} + \frac{\left(3 x^{2} + 10 x + 2\right)^{3}}{x^{2} \left(x^{2} + 5 x + 2\right)^{2}}\right) \operatorname{acot}^{3}{\left(x \right)}}{x \left(x^{2} + 5 x + 2\right)} - \frac{12 \left(6 x + 10 - \frac{\left(3 x^{2} + 10 x + 2\right)^{2}}{x \left(x^{2} + 5 x + 2\right)}\right) \operatorname{acot}^{2}{\left(x \right)}}{x \left(x^{2} + 1\right) \left(x^{2} + 5 x + 2\right)} + \frac{12 \left(2 x \operatorname{acot}{\left(x \right)} + 7\right) \left(3 x^{2} + 10 x + 2\right) \operatorname{acot}{\left(x \right)}}{x \left(x^{2} + 1\right)^{2} \left(x^{2} + 5 x + 2\right)}\right) \operatorname{acot}^{5}{\left(x \right)}
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Gráfico
Derivada de y=arcctg^8lg(x^3+5x^2+2x)
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