Производная 4^(asin(cos(x)))

Вы ввели

 asin(cos(x))
4            

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

Первая производная

  asin(cos(x))               
-4            *log(4)*sin(x) 
-----------------------------
          _____________      
         /        2          
       \/  1 - cos (x)       

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

Вторая производная

              /                         2                 2          \       
 asin(cos(x)) |       cos(x)         sin (x)*cos(x)    sin (x)*log(4)|       
4            *|- ---------------- + ---------------- - --------------|*log(4)
              |     _____________                3/2            2    |       
              |    /        2       /       2   \       -1 + cos (x) |       
              \  \/  1 - cos (x)    \1 - cos (x)/                    /       

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

Третья производная

              /                          2                   2             2       2            2       2                             2                 \              
 asin(cos(x)) |       1               sin (x)           3*cos (x)       log (4)*sin (x)    3*cos (x)*sin (x)   3*cos(x)*log(4)   3*sin (x)*cos(x)*log(4)|              
4            *|---------------- - ---------------- + ---------------- - ---------------- - ----------------- - --------------- - -----------------------|*log(4)*sin(x)
              |   _____________                3/2                3/2                3/2                 5/2             2                         2    |              
              |  /        2       /       2   \      /       2   \      /       2   \       /       2   \        -1 + cos (x)        /        2   \     |              
              \\/  1 - cos (x)    \1 - cos (x)/      \1 - cos (x)/      \1 - cos (x)/       \1 - cos (x)/                            \-1 + cos (x)/     /              

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