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y=(x+5)^7arcctg7x^3

Derivada de y=(x+5)^7arcctg7x^3

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Gráfico:

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Solución

Ha introducido [src]
       7     3     
(x + 5) *acot (7*x)
$$\left(x + 5\right)^{7} \operatorname{acot}^{3}{\left(7 x \right)}$$
(x + 5)^7*acot(7*x)^3
Gráfica
Primera derivada [src]
                                  7     2     
         6     3        21*(x + 5) *acot (7*x)
7*(x + 5) *acot (7*x) - ----------------------
                                      2       
                              1 + 49*x        
$$- \frac{21 \left(x + 5\right)^{7} \operatorname{acot}^{2}{\left(7 x \right)}}{49 x^{2} + 1} + 7 \left(x + 5\right)^{6} \operatorname{acot}^{3}{\left(7 x \right)}$$
Segunda derivada [src]
            /                                            2                    \          
          5 |    2        7*(5 + x)*acot(7*x)   7*(5 + x) *(1 + 7*x*acot(7*x))|          
42*(5 + x) *|acot (7*x) - ------------------- + ------------------------------|*acot(7*x)
            |                          2                            2         |          
            |                  1 + 49*x                  /        2\          |          
            \                                            \1 + 49*x /          /          
$$42 \left(x + 5\right)^{5} \left(\frac{7 \left(x + 5\right)^{2} \left(7 x \operatorname{acot}{\left(7 x \right)} + 1\right)}{\left(49 x^{2} + 1\right)^{2}} - \frac{7 \left(x + 5\right) \operatorname{acot}{\left(7 x \right)}}{49 x^{2} + 1} + \operatorname{acot}^{2}{\left(7 x \right)}\right) \operatorname{acot}{\left(7 x \right)}$$
Tercera derivada [src]
            /                                                   /                                               2     2     \                                             \
            |                                                 3 |    1           2        42*x*acot(7*x)   196*x *acot (7*x)|                                             |
            |                                       49*(5 + x) *|--------- - acot (7*x) + -------------- + -----------------|                                             |
            |                      2                            |        2                          2                  2    |              2                              |
          4 |      3        63*acot (7*x)*(5 + x)               \1 + 49*x                   1 + 49*x           1 + 49*x     /   147*(5 + x) *(1 + 7*x*acot(7*x))*acot(7*x)|
42*(5 + x) *|5*acot (7*x) - --------------------- - ------------------------------------------------------------------------- + ------------------------------------------|
            |                             2                                                   2                                                           2               |
            |                     1 + 49*x                                         /        2\                                                 /        2\                |
            \                                                                      \1 + 49*x /                                                 \1 + 49*x /                /
$$42 \left(x + 5\right)^{4} \left(- \frac{49 \left(x + 5\right)^{3} \left(\frac{196 x^{2} \operatorname{acot}^{2}{\left(7 x \right)}}{49 x^{2} + 1} + \frac{42 x \operatorname{acot}{\left(7 x \right)}}{49 x^{2} + 1} - \operatorname{acot}^{2}{\left(7 x \right)} + \frac{1}{49 x^{2} + 1}\right)}{\left(49 x^{2} + 1\right)^{2}} + \frac{147 \left(x + 5\right)^{2} \left(7 x \operatorname{acot}{\left(7 x \right)} + 1\right) \operatorname{acot}{\left(7 x \right)}}{\left(49 x^{2} + 1\right)^{2}} - \frac{63 \left(x + 5\right) \operatorname{acot}^{2}{\left(7 x \right)}}{49 x^{2} + 1} + 5 \operatorname{acot}^{3}{\left(7 x \right)}\right)$$
Gráfico
Derivada de y=(x+5)^7arcctg7x^3