Производная acos(sin(x/3))

Вы ввели

    /   /x\\
acos|sin|-||
    \   \3//

$$\operatorname{acos}{\left(\sin{\left(\frac{x}{3} \right)} \right)}$$

d /    /   /x\\\
--|acos|sin|-|||
dx\    \   \3///

$$\frac{d}{d x} \operatorname{acos}{\left(\sin{\left(\frac{x}{3} \right)} \right)}$$

Первая производная

          /x\      
      -cos|-|      
          \3/      
-------------------
      _____________
     /        2/x\ 
3*  /  1 - sin |-| 
  \/           \3/ 

$$- \frac{\cos{\left(\frac{x}{3} \right)}}{3 \sqrt{1 - \sin^{2}{\left(\frac{x}{3} \right)}}}$$

Вторая производная

/         2/x\  \       
|      cos |-|  |       
|          \3/  |    /x\
|1 - -----------|*sin|-|
|           2/x\|    \3/
|    1 - sin |-||       
\            \3//       
------------------------
        _____________   
       /        2/x\    
  9*  /  1 - sin |-|    
    \/           \3/    

$$\frac{\left(1 - \frac{\cos^{2}{\left(\frac{x}{3} \right)}}{1 - \sin^{2}{\left(\frac{x}{3} \right)}}\right) \sin{\left(\frac{x}{3} \right)}}{9 \sqrt{1 - \sin^{2}{\left(\frac{x}{3} \right)}}}$$

Третья производная

/         2/x\           2/x\         2/x\    2/x\\       
|      cos |-|      3*sin |-|    3*cos |-|*sin |-||       
|          \3/            \3/          \3/     \3/|    /x\
|1 - ----------- + ----------- - -----------------|*cos|-|
|           2/x\          2/x\                  2 |    \3/
|    1 - sin |-|   1 - sin |-|     /       2/x\\  |       
|            \3/           \3/     |1 - sin |-||  |       
\                                  \        \3//  /       
----------------------------------------------------------
                          _____________                   
                         /        2/x\                    
                   27*  /  1 - sin |-|                    
                      \/           \3/                    

$$\frac{\left(1 + \frac{3 \sin^{2}{\left(\frac{x}{3} \right)}}{1 - \sin^{2}{\left(\frac{x}{3} \right)}} - \frac{\cos^{2}{\left(\frac{x}{3} \right)}}{1 - \sin^{2}{\left(\frac{x}{3} \right)}} - \frac{3 \sin^{2}{\left(\frac{x}{3} \right)} \cos^{2}{\left(\frac{x}{3} \right)}}{\left(1 - \sin^{2}{\left(\frac{x}{3} \right)}\right)^{2}}\right) \cos{\left(\frac{x}{3} \right)}}{27 \sqrt{1 - \sin^{2}{\left(\frac{x}{3} \right)}}}$$

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