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y=arcctg7x×sin(1/x)
Derivada de la función/ x×sin/ (1/x)/ y=arcctg7x/ y=arcctg7x×sin(1/x)

Derivada de y=arcctg7x×sin(1/x)

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Solución

Ha introducido [src] 
             /1\
acot(7*x)*sin|-|
             \x/
sin⁡(1x)acot⁡(7x)\sin{\left(\frac{1}{x} \right)} \operatorname{acot}{\left(7 x \right)} 
acot(7*x)*sin(1/x)
Gráfica
02468-8-6-4-2-1010-200200
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Primera derivada [src] 
        /1\                /1\
   7*sin|-|   acot(7*x)*cos|-|
        \x/                \x/
- --------- - ----------------
          2           2       
  1 + 49*x           x
−7sin⁡(1x)49x2+1−cos⁡(1x)acot⁡(7x)x2- \frac{7 \sin{\left(\frac{1}{x} \right)}}{49 x^{2} + 1} - \frac{\cos{\left(\frac{1}{x} \right)} \operatorname{acot}{\left(7 x \right)}}{x^{2}}
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Segunda derivada [src] 
/              /1\\                                          
|           sin|-||                                          
|     /1\      \x/|                     /1\               /1\
|2*cos|-| - ------|*acot(7*x)     14*cos|-|      686*x*sin|-|
\     \x/     x   /                     \x/               \x/
----------------------------- + -------------- + ------------
               3                 2 /        2\              2
              x                 x *\1 + 49*x /   /        2\ 
                                                 \1 + 49*x /
686xsin⁡(1x)(49x2+1)2+14cos⁡(1x)x2(49x2+1)+(2cos⁡(1x)−sin⁡(1x)x)acot⁡(7x)x3\frac{686 x \sin{\left(\frac{1}{x} \right)}}{\left(49 x^{2} + 1\right)^{2}} + \frac{14 \cos{\left(\frac{1}{x} \right)}}{x^{2} \left(49 x^{2} + 1\right)} + \frac{\left(2 \cos{\left(\frac{1}{x} \right)} - \frac{\sin{\left(\frac{1}{x} \right)}}{x}\right) \operatorname{acot}{\left(7 x \right)}}{x^{3}}
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Tercera derivada [src] 
/                /1\        /1\\                                                                                  
|             cos|-|   6*sin|-||                                  /            2 \             /              /1\\
|       /1\      \x/        \x/|                                  |       196*x  |    /1\      |           sin|-||
|- 6*cos|-| + ------ + --------|*acot(7*x)            /1\     686*|-1 + ---------|*sin|-|      |     /1\      \x/|
|       \x/      2        x    |              2058*cos|-|         |             2|    \x/   21*|2*cos|-| - ------|
\               x              /                      \x/         \     1 + 49*x /             \     \x/     x   /
------------------------------------------ - -------------- - --------------------------- - ----------------------
                     4                                    2                      2               3 /        2\    
                    x                          /        2\            /        2\               x *\1 + 49*x /    
                                             x*\1 + 49*x /            \1 + 49*x /
−686(196x249x2+1−1)sin⁡(1x)(49x2+1)2−2058cos⁡(1x)x(49x2+1)2−21(2cos⁡(1x)−sin⁡(1x)x)x3(49x2+1)+(−6cos⁡(1x)+6sin⁡(1x)x+cos⁡(1x)x2)acot⁡(7x)x4- \frac{686 \left(\frac{196 x^{2}}{49 x^{2} + 1} - 1\right) \sin{\left(\frac{1}{x} \right)}}{\left(49 x^{2} + 1\right)^{2}} - \frac{2058 \cos{\left(\frac{1}{x} \right)}}{x \left(49 x^{2} + 1\right)^{2}} - \frac{21 \left(2 \cos{\left(\frac{1}{x} \right)} - \frac{\sin{\left(\frac{1}{x} \right)}}{x}\right)}{x^{3} \left(49 x^{2} + 1\right)} + \frac{\left(- 6 \cos{\left(\frac{1}{x} \right)} + \frac{6 \sin{\left(\frac{1}{x} \right)}}{x} + \frac{\cos{\left(\frac{1}{x} \right)}}{x^{2}}\right) \operatorname{acot}{\left(7 x \right)}}{x^{4}}
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Gráfico
Derivada de y=arcctg7x×sin(1/x)
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