Производная 4^x*asin(x)

Вы ввели

 x        
4 *asin(x)

$$4^{x} \operatorname{asin}{\left(x \right)}$$

d / x        \
--\4 *asin(x)/
dx            

$$\frac{d}{d x} 4^{x} \operatorname{asin}{\left(x \right)}$$

Первая производная

      x                        
     4         x               
----------- + 4 *asin(x)*log(4)
   ________                    
  /      2                     
\/  1 - x                      

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

Вторая производная

 x /     x           2                2*log(4) \
4 *|----------- + log (4)*asin(x) + -----------|
   |        3/2                        ________|
   |/     2\                          /      2 |
   \\1 - x /                        \/  1 - x  /

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

Третья производная

   /                            2                             \
   |                         3*x                              |
   |                  -1 + -------                            |
   |                             2         2                  |
 x |   3                   -1 + x     3*log (4)     3*x*log(4)|
4 *|log (4)*asin(x) - ------------ + ----------- + -----------|
   |                          3/2       ________           3/2|
   |                  /     2\         /      2    /     2\   |
   \                  \1 - x /       \/  1 - x     \1 - x /   /

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

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