Производная asin(log(x)^5)

Вы ввели

    /   5   \
asin\log (x)/

$$\operatorname{asin}{\left(\log{\left(x \right)}^{5} \right)}$$

d /    /   5   \\
--\asin\log (x)//
dx               

$$\frac{d}{d x} \operatorname{asin}{\left(\log{\left(x \right)}^{5} \right)}$$

Первая производная

          4        
     5*log (x)     
-------------------
     ______________
    /        10    
x*\/  1 - log  (x) 

$$\frac{5 \log{\left(x \right)}^{4}}{x \sqrt{1 - \log{\left(x \right)}^{10}}}$$

Вторая производная

          /                   10    \
     3    |              5*log  (x) |
5*log (x)*|4 - log(x) + ------------|
          |                    10   |
          \             1 - log  (x)/
-------------------------------------
               ______________        
          2   /        10            
         x *\/  1 - log  (x)         

$$\frac{5 \left(- \log{\left(x \right)} + 4 + \frac{5 \log{\left(x \right)}^{10}}{1 - \log{\left(x \right)}^{10}}\right) \log{\left(x \right)}^{3}}{x^{2} \sqrt{1 - \log{\left(x \right)}^{10}}}$$

Третья производная

          /                                   11               20              10    \
     2    |                      2      15*log  (x)      75*log  (x)     85*log  (x) |
5*log (x)*|12 - 12*log(x) + 2*log (x) - ------------ + --------------- + ------------|
          |                                    10                    2          10   |
          |                             1 - log  (x)   /       10   \    1 - log  (x)|
          \                                            \1 - log  (x)/                /
--------------------------------------------------------------------------------------
                                       ______________                                 
                                  3   /        10                                     
                                 x *\/  1 - log  (x)                                  

$$\frac{5 \cdot \left(2 \log{\left(x \right)}^{2} - 12 \log{\left(x \right)} + 12 - \frac{15 \log{\left(x \right)}^{11}}{1 - \log{\left(x \right)}^{10}} + \frac{85 \log{\left(x \right)}^{10}}{1 - \log{\left(x \right)}^{10}} + \frac{75 \log{\left(x \right)}^{20}}{\left(1 - \log{\left(x \right)}^{10}\right)^{2}}\right) \log{\left(x \right)}^{2}}{x^{3} \sqrt{1 - \log{\left(x \right)}^{10}}}$$

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