Производная acot(sin(x))

Вы ввели

acot(sin(x))

$$\operatorname{acot}{\left(\sin{\left(x \right)} \right)}$$

d               
--(acot(sin(x)))
dx              

$$\frac{d}{d x} \operatorname{acot}{\left(\sin{\left(x \right)} \right)}$$

Первая производная

  -cos(x)  
-----------
       2   
1 + sin (x)

$$- \frac{\cos{\left(x \right)}}{\sin^{2}{\left(x \right)} + 1}$$

Вторая производная

/          2    \       
|     2*cos (x) |       
|1 + -----------|*sin(x)
|           2   |       
\    1 + sin (x)/       
------------------------
             2          
      1 + sin (x)       

$$\frac{\left(1 + \frac{2 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)} + 1}\right) \sin{\left(x \right)}}{\sin^{2}{\left(x \right)} + 1}$$

Третья производная

/          2             2            2       2   \       
|     6*sin (x)     2*cos (x)    8*cos (x)*sin (x)|       
|1 - ----------- + ----------- - -----------------|*cos(x)
|           2             2                     2 |       
|    1 + sin (x)   1 + sin (x)     /       2   \  |       
\                                  \1 + sin (x)/  /       
----------------------------------------------------------
                              2                           
                       1 + sin (x)                        

$$\frac{\left(1 - \frac{6 \sin^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)} + 1} + \frac{2 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)} + 1} - \frac{8 \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{\left(\sin^{2}{\left(x \right)} + 1\right)^{2}}\right) \cos{\left(x \right)}}{\sin^{2}{\left(x \right)} + 1}$$

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