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y=arcctg(9x^2+7x+5)

Derivada de y=arcctg(9x^2+7x+5)

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Gráfico:

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Solución

Ha introducido [src]
    /   2          \
acot\9*x  + 7*x + 5/
$$\operatorname{acot}{\left(\left(9 x^{2} + 7 x\right) + 5 \right)}$$
acot(9*x^2 + 7*x + 5)
Gráfica
Primera derivada [src]
     -(7 + 18*x)     
---------------------
                    2
    /   2          \ 
1 + \9*x  + 7*x + 5/ 
$$- \frac{18 x + 7}{\left(\left(9 x^{2} + 7 x\right) + 5\right)^{2} + 1}$$
Segunda derivada [src]
  /               2 /             2\\
  |     (7 + 18*x) *\5 + 7*x + 9*x /|
2*|-9 + ----------------------------|
  |                            2    |
  |            /             2\     |
  \        1 + \5 + 7*x + 9*x /     /
-------------------------------------
                            2        
            /             2\         
        1 + \5 + 7*x + 9*x /         
$$\frac{2 \left(\frac{\left(18 x + 7\right)^{2} \left(9 x^{2} + 7 x + 5\right)}{\left(9 x^{2} + 7 x + 5\right)^{2} + 1} - 9\right)}{\left(9 x^{2} + 7 x + 5\right)^{2} + 1}$$
Tercera derivada [src]
             /                                                                   2\
             |                                                 2 /             2\ |
             |                2                2   4*(7 + 18*x) *\5 + 7*x + 9*x / |
2*(7 + 18*x)*|270 + (7 + 18*x)  + 378*x + 486*x  - -------------------------------|
             |                                                              2     |
             |                                              /             2\      |
             \                                          1 + \5 + 7*x + 9*x /      /
-----------------------------------------------------------------------------------
                                                     2                             
                              /                    2\                              
                              |    /             2\ |                              
                              \1 + \5 + 7*x + 9*x / /                              
$$\frac{2 \left(18 x + 7\right) \left(486 x^{2} + 378 x + \left(18 x + 7\right)^{2} - \frac{4 \left(18 x + 7\right)^{2} \left(9 x^{2} + 7 x + 5\right)^{2}}{\left(9 x^{2} + 7 x + 5\right)^{2} + 1} + 270\right)}{\left(\left(9 x^{2} + 7 x + 5\right)^{2} + 1\right)^{2}}$$
Gráfico
Derivada de y=arcctg(9x^2+7x+5)