Производная log(3,(x^2)+14*x+130)+3

Вы ввели

   /    2             \    
log\3, x  + 14*x + 130/ + 3

$$\log{\left(3 \right)} + 3$$

d /   /    2             \    \
--\log\3, x  + 14*x + 130/ + 3/
dx                             

$$\frac{d}{d x} \left(\log{\left(3 \right)} + 3\right)$$

Первая производная

           /  d  /  log(3) \\|                    
(14 + 2*x)*|-----|---------|||      2             
           \dxi_2\log(xi_2)//|xi_2=x  + 14*x + 130

$$\left(2 x + 14\right) \left. \frac{d}{d \xi_{2}} \frac{\log{\left(3 \right)}}{\log{\left(\xi_{2} \right)}} \right|_{\substack{ \xi_{2}=x^{2} + 14 x + 130 }}$$

Вторая производная

  /         2 /             2          \                                                 \
  |2*(7 + x) *|1 + --------------------|*log(3)                                          |
  |           |       /       2       \|                                                 |
  |           \    log\130 + x  + 14*x//          /  d  /  log(3) \\|                    |
2*|-------------------------------------------- + |-----|---------|||      2             |
  |                   2                           \dxi_2\log(xi_2)//|xi_2=x  + 14*x + 130|
  |  /       2       \     2/       2       \                                            |
  \  \130 + x  + 14*x/ *log \130 + x  + 14*x/                                            /

$$2 \cdot \left(\frac{2 \cdot \left(1 + \frac{2}{\log{\left(x^{2} + 14 x + 130 \right)}}\right) \left(x + 7\right)^{2} \log{\left(3 \right)}}{\left(x^{2} + 14 x + 130\right)^{2} \log{\left(x^{2} + 14 x + 130 \right)}^{2}} + \left. \frac{d}{d \xi_{2}} \frac{\log{\left(3 \right)}}{\log{\left(\xi_{2} \right)}} \right|_{\substack{ \xi_{2}=x^{2} + 14 x + 130 }}\right)$$

Третья производная

          /                                                                              2 /             2          \            2 /             2          \ \       
          |                                                                     4*(7 + x) *|1 + --------------------|   4*(7 + x) *|1 + --------------------| |       
          |                                                   2                            |       /       2       \|              |       /       2       \| |       
          |             6                            4*(7 + x)                             \    log\130 + x  + 14*x//              \    log\130 + x  + 14*x// |       
4*(7 + x)*|3 + -------------------- - --------------------------------------- - ------------------------------------- - --------------------------------------|*log(3)
          |       /       2       \   /       2       \    2/       2       \                     2                     /       2       \    /       2       \|       
          \    log\130 + x  + 14*x/   \130 + x  + 14*x/*log \130 + x  + 14*x/              130 + x  + 14*x              \130 + x  + 14*x/*log\130 + x  + 14*x//       
----------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                2                                                                                     
                                                               /       2       \     2/       2       \                                                               
                                                               \130 + x  + 14*x/ *log \130 + x  + 14*x/                                                               

$$\frac{4 \left(x + 7\right) \left(- \frac{4 \cdot \left(1 + \frac{2}{\log{\left(x^{2} + 14 x + 130 \right)}}\right) \left(x + 7\right)^{2}}{x^{2} + 14 x + 130} - \frac{4 \cdot \left(1 + \frac{2}{\log{\left(x^{2} + 14 x + 130 \right)}}\right) \left(x + 7\right)^{2}}{\left(x^{2} + 14 x + 130\right) \log{\left(x^{2} + 14 x + 130 \right)}} - \frac{4 \left(x + 7\right)^{2}}{\left(x^{2} + 14 x + 130\right) \log{\left(x^{2} + 14 x + 130 \right)}^{2}} + 3 + \frac{6}{\log{\left(x^{2} + 14 x + 130 \right)}}\right) \log{\left(3 \right)}}{\left(x^{2} + 14 x + 130\right)^{2} \log{\left(x^{2} + 14 x + 130 \right)}^{2}}$$

График