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y=(x−7)^4⋅arcctg^2(7x)

Derivada de y=(x−7)^4⋅arcctg^2(7x)

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Gráfico:

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Solución

Ha introducido [src]
       4     2     
(x - 7) *acot (7*x)
$$\left(x - 7\right)^{4} \operatorname{acot}^{2}{\left(7 x \right)}$$
(x - 7)^4*acot(7*x)^2
Gráfica
Primera derivada [src]
                                  4          
         3     2        14*(x - 7) *acot(7*x)
4*(x - 7) *acot (7*x) - ---------------------
                                      2      
                              1 + 49*x       
$$- \frac{14 \left(x - 7\right)^{4} \operatorname{acot}{\left(7 x \right)}}{49 x^{2} + 1} + 4 \left(x - 7\right)^{3} \operatorname{acot}^{2}{\left(7 x \right)}$$
Segunda derivada [src]
            /                                                  2                     \
          2 |      2        56*(-7 + x)*acot(7*x)   49*(-7 + x) *(1 + 14*x*acot(7*x))|
2*(-7 + x) *|6*acot (7*x) - --------------------- + ---------------------------------|
            |                             2                               2          |
            |                     1 + 49*x                     /        2\           |
            \                                                  \1 + 49*x /           /
$$2 \left(x - 7\right)^{2} \left(\frac{49 \left(x - 7\right)^{2} \left(14 x \operatorname{acot}{\left(7 x \right)} + 1\right)}{\left(49 x^{2} + 1\right)^{2}} - \frac{56 \left(x - 7\right) \operatorname{acot}{\left(7 x \right)}}{49 x^{2} + 1} + 6 \operatorname{acot}^{2}{\left(7 x \right)}\right)$$
Tercera derivada [src]
           /                             /                              2          \                                                              \
           |                           3 |                21*x     196*x *acot(7*x)|                                                              |
           |               343*(-7 + x) *|-acot(7*x) + --------- + ----------------|                                                              |
           |                             |                     2              2    |                                        2                     |
           |      2                      \             1 + 49*x       1 + 49*x     /   126*(-7 + x)*acot(7*x)   294*(-7 + x) *(1 + 14*x*acot(7*x))|
4*(-7 + x)*|6*acot (7*x) - --------------------------------------------------------- - ---------------------- + ----------------------------------|
           |                                                 2                                       2                                2           |
           |                                      /        2\                                1 + 49*x                      /        2\            |
           \                                      \1 + 49*x /                                                              \1 + 49*x /            /
$$4 \left(x - 7\right) \left(- \frac{343 \left(x - 7\right)^{3} \left(\frac{196 x^{2} \operatorname{acot}{\left(7 x \right)}}{49 x^{2} + 1} + \frac{21 x}{49 x^{2} + 1} - \operatorname{acot}{\left(7 x \right)}\right)}{\left(49 x^{2} + 1\right)^{2}} + \frac{294 \left(x - 7\right)^{2} \left(14 x \operatorname{acot}{\left(7 x \right)} + 1\right)}{\left(49 x^{2} + 1\right)^{2}} - \frac{126 \left(x - 7\right) \operatorname{acot}{\left(7 x \right)}}{49 x^{2} + 1} + 6 \operatorname{acot}^{2}{\left(7 x \right)}\right)$$
Gráfico
Derivada de y=(x−7)^4⋅arcctg^2(7x)