Производная (tan(x))*(asin(x))

Вы ввели

tan(x)*asin(x)

$$\tan{\left (x \right )} \operatorname{asin}{\left (x \right )}$$

Первая производная

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

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

Вторая производная

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

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

Третья производная

                             2               /       2   \      2                                              /       2   \       
   tan(x)       /       2   \            3*x*\1 + tan (x)/   3*x *tan(x)        2    /       2   \           6*\1 + tan (x)/*tan(x)
----------- + 2*\1 + tan (x)/ *asin(x) + ----------------- + ----------- + 4*tan (x)*\1 + tan (x)/*asin(x) + ----------------------
        3/2                                         3/2              5/2                                             ________      
/     2\                                    /     2\         /     2\                                               /      2       
\1 - x /                                    \1 - x /         \1 - x /                                             \/  1 - x        

$$\frac{3 x^{2} \tan{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} + \frac{3 x \left(\tan^{2}{\left (x \right )} + 1\right)}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + 2 \left(\tan^{2}{\left (x \right )} + 1\right)^{2} \operatorname{asin}{\left (x \right )} + 4 \left(\tan^{2}{\left (x \right )} + 1\right) \tan^{2}{\left (x \right )} \operatorname{asin}{\left (x \right )} + \frac{6 \tan{\left (x \right )}}{\sqrt{- x^{2} + 1}} \left(\tan^{2}{\left (x \right )} + 1\right) + \frac{\tan{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}}$$