Производная (log(2,(5*x+3)))

Вы ввели

log(2, 5*x + 3)

$$\log{\left (2,5 x + 3 \right )}$$

Первая производная

  /  d  /  log(2) \\|            
5*|-----|---------|||            
  \dxi_2\log(xi_2)//|xi_2=5*x + 3

$$5 \left. \frac{d}{d \xi_{2}}\left(\frac{\log{\left (2 \right )}}{\log{\left (\xi_{2} \right )}}\right) \right|_{\substack{ \xi_{2}=5 x + 3 }}$$

Вторая производная

   /         2      \       
25*|1 + ------------|*log(2)
   \    log(3 + 5*x)/       
----------------------------
           2    2           
  (3 + 5*x) *log (3 + 5*x)  

$$\frac{25 \left(1 + \frac{2}{\log{\left (5 x + 3 \right )}}\right) \log{\left (2 \right )}}{\left(5 x + 3\right)^{2} \log^{2}{\left (5 x + 3 \right )}}$$

Третья производная

     /                                            2      \       
     |                                   1 + ------------|       
     |          1              2             log(3 + 5*x)|       
-250*|1 + ------------- + ------------ + ----------------|*log(2)
     |       2            log(3 + 5*x)     log(3 + 5*x)  |       
     \    log (3 + 5*x)                                  /       
-----------------------------------------------------------------
                              3    2                             
                     (3 + 5*x) *log (3 + 5*x)                    

$$- \frac{250 \log{\left (2 \right )}}{\left(5 x + 3\right)^{3} \log^{2}{\left (5 x + 3 \right )}} \left(\frac{1 + \frac{2}{\log{\left (5 x + 3 \right )}}}{\log{\left (5 x + 3 \right )}} + 1 + \frac{2}{\log{\left (5 x + 3 \right )}} + \frac{1}{\log^{2}{\left (5 x + 3 \right )}}\right)$$

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