Производная log(3,cos(x))

Вы ввели

log(3, cos(x))

$$\log{\left (3,\cos{\left (x \right )} \right )}$$

Первая производная

 /  d  /  log(3) \\|                  
-|-----|---------|||           *sin(x)
 \dxi_2\log(xi_2)//|xi_2=cos(x)       

$$- \sin{\left (x \right )} \left. \frac{d}{d \xi_{2}}\left(\frac{\log{\left (3 \right )}}{\log{\left (\xi_{2} \right )}}\right) \right|_{\substack{ \xi_{2}=\cos{\left (x \right )} }}$$

Вторая производная

                                             2    /         2     \       
                                          sin (x)*|1 + -----------|*log(3)
  /  d  /  log(3) \\|                             \    log(cos(x))/       
- |-----|---------|||           *cos(x) + --------------------------------
  \dxi_2\log(xi_2)//|xi_2=cos(x)                   2       2              
                                                cos (x)*log (cos(x))      

$$\frac{\left(1 + \frac{2}{\log{\left (\cos{\left (x \right )} \right )}}\right) \log{\left (3 \right )} \sin^{2}{\left (x \right )}}{\log^{2}{\left (\cos{\left (x \right )} \right )} \cos^{2}{\left (x \right )}} - \cos{\left (x \right )} \left. \frac{d}{d \xi_{2}}\left(\frac{\log{\left (3 \right )}}{\log{\left (\xi_{2} \right )}}\right) \right|_{\substack{ \xi_{2}=\cos{\left (x \right )} }}$$

Третья производная

/                         /         2     \               2    /         2     \               2    /         2     \                                        \       
|       2               3*|1 + -----------|*log(3)   2*sin (x)*|1 + -----------|*log(3)   2*sin (x)*|1 + -----------|*log(3)                                 |       
|  2*sin (x)*log(3)       \    log(cos(x))/                    \    log(cos(x))/                    \    log(cos(x))/          /  d  /  log(3) \\|           |       
|-------------------- + -------------------------- + ---------------------------------- + ---------------------------------- + |-----|---------|||           |*sin(x)
|   3       4                        2                         3       3                            3       2                  \dxi_2\log(xi_2)//|xi_2=cos(x)|       
\cos (x)*log (cos(x))      cos(x)*log (cos(x))              cos (x)*log (cos(x))                 cos (x)*log (cos(x))                                        /       

$$\left(\frac{2 \left(1 + \frac{2}{\log{\left (\cos{\left (x \right )} \right )}}\right) \log{\left (3 \right )} \sin^{2}{\left (x \right )}}{\log^{2}{\left (\cos{\left (x \right )} \right )} \cos^{3}{\left (x \right )}} + \frac{3 \left(1 + \frac{2}{\log{\left (\cos{\left (x \right )} \right )}}\right) \log{\left (3 \right )}}{\log^{2}{\left (\cos{\left (x \right )} \right )} \cos{\left (x \right )}} + \frac{2 \left(1 + \frac{2}{\log{\left (\cos{\left (x \right )} \right )}}\right) \log{\left (3 \right )} \sin^{2}{\left (x \right )}}{\log^{3}{\left (\cos{\left (x \right )} \right )} \cos^{3}{\left (x \right )}} + \left. \frac{d}{d \xi_{2}}\left(\frac{\log{\left (3 \right )}}{\log{\left (\xi_{2} \right )}}\right) \right|_{\substack{ \xi_{2}=\cos{\left (x \right )} }} + \frac{2 \log{\left (3 \right )} \sin^{2}{\left (x \right )}}{\log^{4}{\left (\cos{\left (x \right )} \right )} \cos^{3}{\left (x \right )}}\right) \sin{\left (x \right )}$$