Производная 3^coth(x)

Вы ввели

 coth(x)
3       

$$3^{\coth{\left (x \right )}}$$

Первая производная

  coth(x)        
-3       *log(3) 
-----------------
         2       
     sinh (x)    

$$- \frac{3^{\coth{\left (x \right )}} \log{\left (3 \right )}}{\sinh^{2}{\left (x \right )}}$$

Вторая производная

 coth(x) /             log(3)\       
3       *|2*cosh(x) + -------|*log(3)
         \            sinh(x)/       
-------------------------------------
                   3                 
               sinh (x)              

$$\frac{3^{\coth{\left (x \right )}} \log{\left (3 \right )}}{\sinh^{3}{\left (x \right )}} \left(2 \cosh{\left (x \right )} + \frac{\log{\left (3 \right )}}{\sinh{\left (x \right )}}\right)$$

Третья производная

         /       2             2                      \       
 coth(x) |    log (3)    6*cosh (x)   6*cosh(x)*log(3)|       
3       *|2 - -------- - ---------- - ----------------|*log(3)
         |        4           2               3       |       
         \    sinh (x)    sinh (x)        sinh (x)    /       
--------------------------------------------------------------
                               2                              
                           sinh (x)                           

$$\frac{3^{\coth{\left (x \right )}} \log{\left (3 \right )}}{\sinh^{2}{\left (x \right )}} \left(2 - \frac{6 \cosh^{2}{\left (x \right )}}{\sinh^{2}{\left (x \right )}} - \frac{6 \cosh{\left (x \right )}}{\sinh^{3}{\left (x \right )}} \log{\left (3 \right )} - \frac{\log^{2}{\left (3 \right )}}{\sinh^{4}{\left (x \right )}}\right)$$