Производная log(asin(3*x))

Вы ввели

log(asin(3*x))

$$\log{\left (\operatorname{asin}{\left (3 x \right )} \right )}$$

Первая производная

           3           
-----------------------
   __________          
  /        2           
\/  1 - 9*x  *asin(3*x)

$$\frac{3}{\sqrt{- 9 x^{2} + 1} \operatorname{asin}{\left (3 x \right )}}$$

Вторая производная

  /          1                  3*x     \
9*|--------------------- + -------------|
  |/        2\                       3/2|
  |\-1 + 9*x /*asin(3*x)   /       2\   |
  \                        \1 - 9*x /   /
-----------------------------------------
                asin(3*x)                

$$\frac{1}{\operatorname{asin}{\left (3 x \right )}} \left(\frac{27 x}{\left(- 9 x^{2} + 1\right)^{\frac{3}{2}}} + \frac{9}{\left(9 x^{2} - 1\right) \operatorname{asin}{\left (3 x \right )}}\right)$$

Третья производная

   /                                                   2                             \
   |      1                    2                   27*x                 9*x          |
27*|------------- + ------------------------ + ------------- - ----------------------|
   |          3/2             3/2                        5/2              2          |
   |/       2\      /       2\        2        /       2\      /        2\           |
   \\1 - 9*x /      \1 - 9*x /   *asin (3*x)   \1 - 9*x /      \-1 + 9*x / *asin(3*x)/
--------------------------------------------------------------------------------------
                                      asin(3*x)                                       

$$\frac{1}{\operatorname{asin}{\left (3 x \right )}} \left(\frac{729 x^{2}}{\left(- 9 x^{2} + 1\right)^{\frac{5}{2}}} - \frac{243 x}{\left(9 x^{2} - 1\right)^{2} \operatorname{asin}{\left (3 x \right )}} + \frac{27}{\left(- 9 x^{2} + 1\right)^{\frac{3}{2}}} + \frac{54}{\left(- 9 x^{2} + 1\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left (3 x \right )}}\right)$$