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y=(x-7)^4*arcctg^27x

Derivada de y=(x-7)^4*arcctg^27x

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Gráfico:

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Solución

Ha introducido [src]
       4     27   
(x - 7) *acot  (x)
$$\left(x - 7\right)^{4} \operatorname{acot}^{27}{\left(x \right)}$$
(x - 7)^4*acot(x)^27
Gráfica
Primera derivada [src]
                                 4     26   
         3     27      27*(x - 7) *acot  (x)
4*(x - 7) *acot  (x) - ---------------------
                                    2       
                               1 + x        
$$- \frac{27 \left(x - 7\right)^{4} \operatorname{acot}^{26}{\left(x \right)}}{x^{2} + 1} + 4 \left(x - 7\right)^{3} \operatorname{acot}^{27}{\left(x \right)}$$
Segunda derivada [src]
                      /                                             2                 \
          2     25    |      2      36*(-7 + x)*acot(x)   9*(-7 + x) *(13 + x*acot(x))|
6*(-7 + x) *acot  (x)*|2*acot (x) - ------------------- + ----------------------------|
                      |                         2                          2          |
                      |                    1 + x                   /     2\           |
                      \                                            \1 + x /           /
$$6 \left(x - 7\right)^{2} \left(\frac{9 \left(x - 7\right)^{2} \left(x \operatorname{acot}{\left(x \right)} + 13\right)}{\left(x^{2} + 1\right)^{2}} - \frac{36 \left(x - 7\right) \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + 2 \operatorname{acot}^{2}{\left(x \right)}\right) \operatorname{acot}^{25}{\left(x \right)}$$
Tercera derivada [src]
                     /                                                 /                         2     2                  \                                         \
                     |                                               3 |      2       325     4*x *acot (x)   78*x*acot(x)|                                         |
                     |                                     9*(-7 + x) *|- acot (x) + ------ + ------------- + ------------|                                         |
                     |                     2                           |                  2            2              2   |               2                         |
      24             |      3      162*acot (x)*(-7 + x)               \             1 + x        1 + x          1 + x    /   108*(-7 + x) *(13 + x*acot(x))*acot(x)|
6*acot  (x)*(-7 + x)*|4*acot (x) - --------------------- - ---------------------------------------------------------------- + --------------------------------------|
                     |                          2                                             2                                                     2               |
                     |                     1 + x                                      /     2\                                              /     2\                |
                     \                                                                \1 + x /                                              \1 + x /                /
$$6 \left(x - 7\right) \left(- \frac{9 \left(x - 7\right)^{3} \left(\frac{4 x^{2} \operatorname{acot}^{2}{\left(x \right)}}{x^{2} + 1} + \frac{78 x \operatorname{acot}{\left(x \right)}}{x^{2} + 1} - \operatorname{acot}^{2}{\left(x \right)} + \frac{325}{x^{2} + 1}\right)}{\left(x^{2} + 1\right)^{2}} + \frac{108 \left(x - 7\right)^{2} \left(x \operatorname{acot}{\left(x \right)} + 13\right) \operatorname{acot}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{162 \left(x - 7\right) \operatorname{acot}^{2}{\left(x \right)}}{x^{2} + 1} + 4 \operatorname{acot}^{3}{\left(x \right)}\right) \operatorname{acot}^{24}{\left(x \right)}$$
Gráfico
Derivada de y=(x-7)^4*arcctg^27x