Производная tan(asin(x))

Вы ввели

tan(asin(x))

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

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