Производная log(2,sin(x))

Вы ввели

log(2, sin(x))

$$\log{\left(2 \right)}$$

d                 
--(log(2, sin(x)))
dx                

$$\frac{d}{d x} \log{\left(2 \right)}$$

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

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

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