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y=(x−7)^4⋅arcctg^2(7x)
Derivada de la función/ ctg^2/ y=(x−7)^4⋅arcctg^2(7x)

Derivada de y=(x−7)^4⋅arcctg^2(7x)

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

Ha introducido [src] 
       4     2     
(x - 7) *acot (7*x)
(x−7)4acot⁡2(7x)\left(x - 7\right)^{4} \operatorname{acot}^{2}{\left(7 x \right)} 
(x - 7)^4*acot(7*x)^2
Gráfica
02468-8-6-4-2-1010-5000050000
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Primera derivada [src] 
                                  4          
         3     2        14*(x - 7) *acot(7*x)
4*(x - 7) *acot (7*x) - ---------------------
                                      2      
                              1 + 49*x
−14(x−7)4acot⁡(7x)49x2+1+4(x−7)3acot⁡2(7x)- \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)}
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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(x−7)2(49(x−7)2(14xacot⁡(7x)+1)(49x2+1)2−56(x−7)acot⁡(7x)49x2+1+6acot⁡2(7x))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)
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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(x−7)(−343(x−7)3(196x2acot⁡(7x)49x2+1+21x49x2+1−acot⁡(7x))(49x2+1)2+294(x−7)2(14xacot⁡(7x)+1)(49x2+1)2−126(x−7)acot⁡(7x)49x2+1+6acot⁡2(7x))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)
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Gráfico
Derivada de y=(x−7)^4⋅arcctg^2(7x)
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