Производная log(asin(x))^(2)

Вы ввели

   2         
log (asin(x))

$$\log^{2}{\left (\operatorname{asin}{\left (x \right )} \right )}$$

Первая производная

   2*log(asin(x))  
-------------------
   ________        
  /      2         
\/  1 - x  *asin(x)

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

Вторая производная

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

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

Третья производная

  /                                                                                     2                                  \
  |log(asin(x))            3                2*log(asin(x))             3*x           3*x *log(asin(x))    3*x*log(asin(x)) |
2*|------------ - -------------------- + -------------------- + ------------------ + ----------------- - ------------------|
  |        3/2            3/2                    3/2                     2                      5/2               2        |
  |/     2\       /     2\        2      /     2\        2      /      2\               /     2\         /      2\         |
  \\1 - x /       \1 - x /   *asin (x)   \1 - x /   *asin (x)   \-1 + x / *asin(x)      \1 - x /         \-1 + x / *asin(x)/
----------------------------------------------------------------------------------------------------------------------------
                                                          asin(x)                                                           

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