Производная atan(cos(asin(x)))

Вы ввели

atan(cos(asin(x)))

$$\operatorname{atan}{\left(\cos{\left(\operatorname{asin}{\left(x \right)} \right)} \right)}$$

d                     
--(atan(cos(asin(x))))
dx                    

$$\frac{d}{d x} \operatorname{atan}{\left(\cos{\left(\operatorname{asin}{\left(x \right)} \right)} \right)}$$

Первая производная

              -x               
-------------------------------
                       ________
/       2         \   /      2 
\1 + cos (asin(x))/*\/  1 - x  

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

Вторая производная

                      2                2                   
       1             x              2*x *cos(asin(x))      
- ----------- - ----------- + -----------------------------
     ________           3/2   /       2         \ /      2\
    /      2    /     2\      \1 + cos (asin(x))/*\-1 + x /
  \/  1 - x     \1 - x /                                   
-----------------------------------------------------------
                            2                              
                     1 + cos (asin(x))                     

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

Третья производная

  /                       2                       2                                                          2    2                            2                    \
  |       3            3*x                     2*x                         6*cos(asin(x))                 8*x *cos (asin(x))                6*x *cos(asin(x))       |
x*|- ----------- - ----------- + ------------------------------- + ----------------------------- - -------------------------------- - ------------------------------|
  |          3/2           5/2                               3/2   /       2         \ /      2\                      2         3/2                                2|
  |  /     2\      /     2\      /       2         \ /     2\      \1 + cos (asin(x))/*\-1 + x /   /       2         \  /     2\      /       2         \ /      2\ |
  \  \1 - x /      \1 - x /      \1 + cos (asin(x))/*\1 - x /                                      \1 + cos (asin(x))/ *\1 - x /      \1 + cos (asin(x))/*\-1 + x / /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                 2                                                                                   
                                                                          1 + cos (asin(x))                                                                          

$$\frac{x \left(- \frac{6 x^{2} \cos{\left(\operatorname{asin}{\left(x \right)} \right)}}{\left(x^{2} - 1\right)^{2} \left(\cos^{2}{\left(\operatorname{asin}{\left(x \right)} \right)} + 1\right)} + \frac{2 x^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(\cos^{2}{\left(\operatorname{asin}{\left(x \right)} \right)} + 1\right)} - \frac{8 x^{2} \cos^{2}{\left(\operatorname{asin}{\left(x \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(\cos^{2}{\left(\operatorname{asin}{\left(x \right)} \right)} + 1\right)^{2}} - \frac{3 x^{2}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{6 \cos{\left(\operatorname{asin}{\left(x \right)} \right)}}{\left(x^{2} - 1\right) \left(\cos^{2}{\left(\operatorname{asin}{\left(x \right)} \right)} + 1\right)} - \frac{3}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right)}{\cos^{2}{\left(\operatorname{asin}{\left(x \right)} \right)} + 1}$$

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