Производная acos(tan(5*x))

Вы ввели

acos(tan(5*x))

$$\operatorname{acos}{\left (\tan{\left (5 x \right )} \right )}$$

Первая производная

 /         2     \ 
-\5 + 5*tan (5*x)/ 
-------------------
    _______________
   /        2      
 \/  1 - tan (5*x) 

$$- \frac{5 \tan^{2}{\left (5 x \right )} + 5}{\sqrt{- \tan^{2}{\left (5 x \right )} + 1}}$$

Вторая производная

                    /           2     \         
    /       2     \ |    1 + tan (5*x)|         
-25*\1 + tan (5*x)/*|2 + -------------|*tan(5*x)
                    |           2     |         
                    \    1 - tan (5*x)/         
------------------------------------------------
                  _______________               
                 /        2                     
               \/  1 - tan (5*x)                

$$- \frac{25 \tan{\left (5 x \right )}}{\sqrt{- \tan^{2}{\left (5 x \right )} + 1}} \left(2 + \frac{\tan^{2}{\left (5 x \right )} + 1}{- \tan^{2}{\left (5 x \right )} + 1}\right) \left(\tan^{2}{\left (5 x \right )} + 1\right)$$

Третья производная

                     /                                 2                    2                                        \
                     |                  /       2     \      /       2     \     2             2      /       2     \|
     /       2     \ |         2        \1 + tan (5*x)/    3*\1 + tan (5*x)/ *tan (5*x)   6*tan (5*x)*\1 + tan (5*x)/|
-125*\1 + tan (5*x)/*|2 + 6*tan (5*x) + ---------------- + ---------------------------- + ---------------------------|
                     |                          2                               2                       2            |
                     |                   1 - tan (5*x)           /       2     \                 1 - tan (5*x)       |
                     \                                           \1 - tan (5*x)/                                     /
----------------------------------------------------------------------------------------------------------------------
                                                     _______________                                                  
                                                    /        2                                                        
                                                  \/  1 - tan (5*x)                                                   

$$- \frac{125}{\sqrt{- \tan^{2}{\left (5 x \right )} + 1}} \left(\tan^{2}{\left (5 x \right )} + 1\right) \left(6 \tan^{2}{\left (5 x \right )} + 2 + \frac{\left(\tan^{2}{\left (5 x \right )} + 1\right)^{2}}{- \tan^{2}{\left (5 x \right )} + 1} + \frac{6 \left(\tan^{2}{\left (5 x \right )} + 1\right) \tan^{2}{\left (5 x \right )}}{- \tan^{2}{\left (5 x \right )} + 1} + \frac{3 \left(\tan^{2}{\left (5 x \right )} + 1\right)^{2} \tan^{2}{\left (5 x \right )}}{\left(- \tan^{2}{\left (5 x \right )} + 1\right)^{2}}\right)$$