Производная функции/ От одной переменной/ y' = (log(cos(atan(sinh(x)))))'

Производная log(cos(atan(sinh(x))))

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Решение

Вы ввели [src]
log(cos(atan(sinh(x))))
$$\log{\left (\cos{\left (\operatorname{atan}{\left (\sinh{\left (x \right )} \right )} \right )} \right )}$$
График
Первая производная [src]
         -cosh(x)*sinh(x)           
------------------------------------
              3/2                   
/        2   \                      
\1 + sinh (x)/   *cos(atan(sinh(x)))
$$- \frac{\sinh{\left (x \right )} \cosh{\left (x \right )}}{\left(\sinh^{2}{\left (x \right )} + 1\right)^{\frac{3}{2}} \cos{\left (\operatorname{atan}{\left (\sinh{\left (x \right )} \right )} \right )}}$$
Упростить
Вторая производная [src]
           2                   2                2        2                  2        2            
       cosh (x)            sinh (x)       3*cosh (x)*sinh (x)           cosh (x)*sinh (x)         
- ----------------- - ----------------- + ------------------- - ----------------------------------
                3/2                 3/2                  5/2                  3                   
  /        2   \      /        2   \       /        2   \       /        2   \                    
  \1 + sinh (x)/      \1 + sinh (x)/       \1 + sinh (x)/       \1 + sinh (x)/ *cos(atan(sinh(x)))
--------------------------------------------------------------------------------------------------
                                        cos(atan(sinh(x)))
$$\frac{1}{\cos{\left (\operatorname{atan}{\left (\sinh{\left (x \right )} \right )} \right )}} \left(- \frac{\sinh^{2}{\left (x \right )} \cosh^{2}{\left (x \right )}}{\left(\sinh^{2}{\left (x \right )} + 1\right)^{3} \cos{\left (\operatorname{atan}{\left (\sinh{\left (x \right )} \right )} \right )}} - \frac{\sinh^{2}{\left (x \right )}}{\left(\sinh^{2}{\left (x \right )} + 1\right)^{\frac{3}{2}}} - \frac{\cosh^{2}{\left (x \right )}}{\left(\sinh^{2}{\left (x \right )} + 1\right)^{\frac{3}{2}}} + \frac{3 \sinh^{2}{\left (x \right )} \cosh^{2}{\left (x \right )}}{\left(\sinh^{2}{\left (x \right )} + 1\right)^{\frac{5}{2}}}\right)$$
Упростить
Третья производная [src]
/                                2                   2                2        2                        2                                    2                                 2        2                            2        2           \                
|          4               9*cosh (x)          9*sinh (x)      15*cosh (x)*sinh (x)               3*cosh (x)                           3*sinh (x)                        2*cosh (x)*sinh (x)                   9*cosh (x)*sinh (x)        |                
|- ----------------- + ----------------- + ----------------- - -------------------- - ---------------------------------- - ---------------------------------- - ------------------------------------- + ----------------------------------|*cosh(x)*sinh(x)
|                3/2                 5/2                 5/2                  7/2                   3                                    3                                    9/2                                     4                   |                
|  /        2   \      /        2   \      /        2   \       /        2   \        /        2   \                       /        2   \                       /        2   \       2                  /        2   \                    |                
\  \1 + sinh (x)/      \1 + sinh (x)/      \1 + sinh (x)/       \1 + sinh (x)/        \1 + sinh (x)/ *cos(atan(sinh(x)))   \1 + sinh (x)/ *cos(atan(sinh(x)))   \1 + sinh (x)/   *cos (atan(sinh(x)))   \1 + sinh (x)/ *cos(atan(sinh(x)))/                
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                     cos(atan(sinh(x)))
$$\frac{\sinh{\left (x \right )} \cosh{\left (x \right )}}{\cos{\left (\operatorname{atan}{\left (\sinh{\left (x \right )} \right )} \right )}} \left(- \frac{3 \sinh^{2}{\left (x \right )}}{\left(\sinh^{2}{\left (x \right )} + 1\right)^{3} \cos{\left (\operatorname{atan}{\left (\sinh{\left (x \right )} \right )} \right )}} - \frac{3 \cosh^{2}{\left (x \right )}}{\left(\sinh^{2}{\left (x \right )} + 1\right)^{3} \cos{\left (\operatorname{atan}{\left (\sinh{\left (x \right )} \right )} \right )}} + \frac{9 \sinh^{2}{\left (x \right )} \cosh^{2}{\left (x \right )}}{\left(\sinh^{2}{\left (x \right )} + 1\right)^{4} \cos{\left (\operatorname{atan}{\left (\sinh{\left (x \right )} \right )} \right )}} - \frac{4}{\left(\sinh^{2}{\left (x \right )} + 1\right)^{\frac{3}{2}}} + \frac{9 \sinh^{2}{\left (x \right )}}{\left(\sinh^{2}{\left (x \right )} + 1\right)^{\frac{5}{2}}} + \frac{9 \cosh^{2}{\left (x \right )}}{\left(\sinh^{2}{\left (x \right )} + 1\right)^{\frac{5}{2}}} - \frac{15 \sinh^{2}{\left (x \right )} \cosh^{2}{\left (x \right )}}{\left(\sinh^{2}{\left (x \right )} + 1\right)^{\frac{7}{2}}} - \frac{2 \sinh^{2}{\left (x \right )} \cosh^{2}{\left (x \right )}}{\left(\sinh^{2}{\left (x \right )} + 1\right)^{\frac{9}{2}} \cos^{2}{\left (\operatorname{atan}{\left (\sinh{\left (x \right )} \right )} \right )}}\right)$$
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