Производная log(asin(9*x))

Вы ввели

log(asin(9*x))

$$\log{\left(\operatorname{asin}{\left(9 x \right)} \right)}$$

d                 
--(log(asin(9*x)))
dx                

$$\frac{d}{d x} \log{\left(\operatorname{asin}{\left(9 x \right)} \right)}$$

Первая производная

           9            
------------------------
   ___________          
  /         2           
\/  1 - 81*x  *asin(9*x)

$$\frac{9}{\sqrt{1 - 81 x^{2}} \operatorname{asin}{\left(9 x \right)}}$$

Вторая производная

   /          1                   9*x      \
81*|---------------------- + --------------|
   |/         2\                        3/2|
   |\-1 + 81*x /*asin(9*x)   /        2\   |
   \                         \1 - 81*x /   /
--------------------------------------------
                 asin(9*x)                  

$$\frac{81 \cdot \left(\frac{9 x}{\left(1 - 81 x^{2}\right)^{\frac{3}{2}}} + \frac{1}{\left(81 x^{2} - 1\right) \operatorname{asin}{\left(9 x \right)}}\right)}{\operatorname{asin}{\left(9 x \right)}}$$

Третья производная

    /                                                      2                              \
    |      1                      2                   243*x                  27*x         |
729*|-------------- + ------------------------- + -------------- - -----------------------|
    |           3/2              3/2                         5/2               2          |
    |/        2\      /        2\        2        /        2\      /         2\           |
    \\1 - 81*x /      \1 - 81*x /   *asin (9*x)   \1 - 81*x /      \-1 + 81*x / *asin(9*x)/
-------------------------------------------------------------------------------------------
                                         asin(9*x)                                         

$$\frac{729 \cdot \left(\frac{243 x^{2}}{\left(1 - 81 x^{2}\right)^{\frac{5}{2}}} - \frac{27 x}{\left(81 x^{2} - 1\right)^{2} \operatorname{asin}{\left(9 x \right)}} + \frac{1}{\left(1 - 81 x^{2}\right)^{\frac{3}{2}}} + \frac{2}{\left(1 - 81 x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left(9 x \right)}}\right)}{\operatorname{asin}{\left(9 x \right)}}$$

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