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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