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y=arctan(4x^-9+pix)
Derivada de la función/ arctan/ y=arctan(4x^-9+pix)

Derivada de y=arctan(4x^-9+pix)

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

Ha introducido [src] 
    /4        \
atan|-- + pi*x|
    | 9       |
    \x        /
atan⁡(πx+4x9)\operatorname{atan}{\left(\pi x + \frac{4}{x^{9}} \right)} 
atan(4/x^9 + pi*x)
Gráfica
02468-8-6-4-2-10105-5
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Primera derivada [src] 
          36    
    pi - ---    
          10    
         x      
----------------
               2
    /4        \ 
1 + |-- + pi*x| 
    | 9       | 
    \x        /
π−36x10(πx+4x9)2+1\frac{\pi - \frac{36}{x^{10}}}{\left(\pi x + \frac{4}{x^{9}}\right)^{2} + 1}
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Segunda derivada [src] 
  /                2            \
  |      /      36\  /4        \|
  |      |pi - ---| *|-- + pi*x||
  |      |      10|  | 9       ||
  |180   \     x  /  \x        /|
2*|--- - -----------------------|
  | 11                      2   |
  |x             /4        \    |
  |          1 + |-- + pi*x|    |
  |              | 9       |    |
  \              \x        /    /
---------------------------------
                        2        
             /4        \         
         1 + |-- + pi*x|         
             | 9       |         
             \x        /
2(−(π−36x10)2(πx+4x9)(πx+4x9)2+1+180x11)(πx+4x9)2+1\frac{2 \left(- \frac{\left(\pi - \frac{36}{x^{10}}\right)^{2} \left(\pi x + \frac{4}{x^{9}}\right)}{\left(\pi x + \frac{4}{x^{9}}\right)^{2} + 1} + \frac{180}{x^{11}}\right)}{\left(\pi x + \frac{4}{x^{9}}\right)^{2} + 1}
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Tercera derivada [src] 
  /                     3                  3            2                              \
  |           /      36\         /      36\  /4        \         /      36\ /4        \|
  |           |pi - ---|       4*|pi - ---| *|-- + pi*x|    1080*|pi - ---|*|-- + pi*x||
  |           |      10|         |      10|  | 9       |         |      10| | 9       ||
  |  1980     \     x  /         \     x  /  \x        /         \     x  / \x        /|
2*|- ---- - ---------------- + -------------------------- - ---------------------------|
  |   12                   2                        2              /               2\  |
  |  x          /4        \       /               2\            11 |    /4        \ |  |
  |         1 + |-- + pi*x|       |    /4        \ |           x  *|1 + |-- + pi*x| |  |
  |             | 9       |       |1 + |-- + pi*x| |               |    | 9       | |  |
  |             \x        /       |    | 9       | |               \    \x        / /  |
  \                               \    \x        / /                                   /
----------------------------------------------------------------------------------------
                                                   2                                    
                                        /4        \                                     
                                    1 + |-- + pi*x|                                     
                                        | 9       |                                     
                                        \x        /
2(4(π−36x10)3(πx+4x9)2((πx+4x9)2+1)2−(π−36x10)3(πx+4x9)2+1−1080(π−36x10)(πx+4x9)x11((πx+4x9)2+1)−1980x12)(πx+4x9)2+1\frac{2 \left(\frac{4 \left(\pi - \frac{36}{x^{10}}\right)^{3} \left(\pi x + \frac{4}{x^{9}}\right)^{2}}{\left(\left(\pi x + \frac{4}{x^{9}}\right)^{2} + 1\right)^{2}} - \frac{\left(\pi - \frac{36}{x^{10}}\right)^{3}}{\left(\pi x + \frac{4}{x^{9}}\right)^{2} + 1} - \frac{1080 \left(\pi - \frac{36}{x^{10}}\right) \left(\pi x + \frac{4}{x^{9}}\right)}{x^{11} \left(\left(\pi x + \frac{4}{x^{9}}\right)^{2} + 1\right)} - \frac{1980}{x^{12}}\right)}{\left(\pi x + \frac{4}{x^{9}}\right)^{2} + 1}
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Gráfico
Derivada de y=arctan(4x^-9+pix)
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