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y=(sin9x)/(ctg(2x+1))
Derivada de la función/ sin9x/ (2x+1)/ y=(sin9x)/(ctg(2x+1))

Derivada de y=(sin9x)/(ctg(2x+1))

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

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Solución

Ha introducido [src] 
  sin(9*x)  
------------
cot(2*x + 1)
sin⁡(9x)cot⁡(2x+1)\frac{\sin{\left(9 x \right)}}{\cot{\left(2 x + 1 \right)}} 
sin(9*x)/cot(2*x + 1)
Gráfica
02468-8-6-4-2-1010-5000050000
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Primera derivada [src] 
               /         2         \         
 9*cos(9*x)    \2 + 2*cot (2*x + 1)/*sin(9*x)
------------ + ------------------------------
cot(2*x + 1)              2                  
                       cot (2*x + 1)
(2cot⁡2(2x+1)+2)sin⁡(9x)cot⁡2(2x+1)+9cos⁡(9x)cot⁡(2x+1)\frac{\left(2 \cot^{2}{\left(2 x + 1 \right)} + 2\right) \sin{\left(9 x \right)}}{\cot^{2}{\left(2 x + 1 \right)}} + \frac{9 \cos{\left(9 x \right)}}{\cot{\left(2 x + 1 \right)}}
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Segunda derivada [src] 
                                     /            2         \               /       2         \         
                 /       2         \ |     1 + cot (1 + 2*x)|            36*\1 + cot (1 + 2*x)/*cos(9*x)
-81*sin(9*x) + 8*\1 + cot (1 + 2*x)/*|-1 + -----------------|*sin(9*x) + -------------------------------
                                     |          2           |                      cot(1 + 2*x)         
                                     \       cot (1 + 2*x)  /                                           
--------------------------------------------------------------------------------------------------------
                                              cot(1 + 2*x)
8(cot⁡2(2x+1)+1cot⁡2(2x+1)−1)(cot⁡2(2x+1)+1)sin⁡(9x)+36(cot⁡2(2x+1)+1)cos⁡(9x)cot⁡(2x+1)−81sin⁡(9x)cot⁡(2x+1)\frac{8 \left(\frac{\cot^{2}{\left(2 x + 1 \right)} + 1}{\cot^{2}{\left(2 x + 1 \right)}} - 1\right) \left(\cot^{2}{\left(2 x + 1 \right)} + 1\right) \sin{\left(9 x \right)} + \frac{36 \left(\cot^{2}{\left(2 x + 1 \right)} + 1\right) \cos{\left(9 x \right)}}{\cot{\left(2 x + 1 \right)}} - 81 \sin{\left(9 x \right)}}{\cot{\left(2 x + 1 \right)}}
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Tercera derivada [src] 
                                                                                                                                                                  /            2         \         
                                                                                                                                              /       2         \ |     1 + cot (1 + 2*x)|         
                    /                                           2                        3\                                               216*\1 + cot (1 + 2*x)/*|-1 + -----------------|*cos(9*x)
                    |                        /       2         \      /       2         \ |                /       2         \                                    |          2           |         
  729*cos(9*x)      |         2            5*\1 + cot (1 + 2*x)/    3*\1 + cot (1 + 2*x)/ |            486*\1 + cot (1 + 2*x)/*sin(9*x)                           \       cot (1 + 2*x)  /         
- ------------ + 16*|2 + 2*cot (1 + 2*x) - ---------------------- + ----------------------|*sin(9*x) - -------------------------------- + ---------------------------------------------------------
  cot(1 + 2*x)      |                             2                        4              |                        2                                             cot(1 + 2*x)                      
                    \                          cot (1 + 2*x)            cot (1 + 2*x)     /                     cot (1 + 2*x)
216(cot⁡2(2x+1)+1cot⁡2(2x+1)−1)(cot⁡2(2x+1)+1)cos⁡(9x)cot⁡(2x+1)−486(cot⁡2(2x+1)+1)sin⁡(9x)cot⁡2(2x+1)+16(3(cot⁡2(2x+1)+1)3cot⁡4(2x+1)−5(cot⁡2(2x+1)+1)2cot⁡2(2x+1)+2cot⁡2(2x+1)+2)sin⁡(9x)−729cos⁡(9x)cot⁡(2x+1)\frac{216 \left(\frac{\cot^{2}{\left(2 x + 1 \right)} + 1}{\cot^{2}{\left(2 x + 1 \right)}} - 1\right) \left(\cot^{2}{\left(2 x + 1 \right)} + 1\right) \cos{\left(9 x \right)}}{\cot{\left(2 x + 1 \right)}} - \frac{486 \left(\cot^{2}{\left(2 x + 1 \right)} + 1\right) \sin{\left(9 x \right)}}{\cot^{2}{\left(2 x + 1 \right)}} + 16 \left(\frac{3 \left(\cot^{2}{\left(2 x + 1 \right)} + 1\right)^{3}}{\cot^{4}{\left(2 x + 1 \right)}} - \frac{5 \left(\cot^{2}{\left(2 x + 1 \right)} + 1\right)^{2}}{\cot^{2}{\left(2 x + 1 \right)}} + 2 \cot^{2}{\left(2 x + 1 \right)} + 2\right) \sin{\left(9 x \right)} - \frac{729 \cos{\left(9 x \right)}}{\cot{\left(2 x + 1 \right)}}
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Gráfico
Derivada de y=(sin9x)/(ctg(2x+1))
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