Производная функции/ От одной переменной/ y' = (log(sin(x),tan(x)))'

Производная log(sin(x),tan(x))

Учитель очень удивится увидев твоё верное решение производной 😼

()'

– производная -го порядка в точке

Примеры

График:

от до

Кусочно-заданная:

{ кусочно-заданную функцию ввести здесь.

Виды выражений

обычное уравнение log(sin(x),tan(x)) = 0
неявная функция log(sin(x),tan(x))
производная неявной log(sin(x),tan(x))
канонический вид log(sin(x),tan(x))
система уравнений log(sin(x),tan(x))
Неопределенный интеграл log(sin(x),tan(x))
построить график log(sin(x),tan(x))
предел функции log(sin(x),tan(x))
упростить выражение log(sin(x),tan(x))

Решение

Вы ввели [src]
log(sin(x), tan(x))
$$\log{\left(\sin{\left(x \right)} \right)}$$
d                      
--(log(sin(x), tan(x)))
dx
$$\frac{d}{d x} \log{\left(\sin{\left(x \right)} \right)}$$
Преобразовать
График
Построить график f(x)
Построить график f'(x)
Первая производная [src]
cos(x)   /       2   \ /  d  /log(sin(x))\\|           
------ + \1 + tan (x)/*|-----|-----------|||           
sin(x)                 \dxi_2\ log(xi_2) //|xi_2=tan(x)
$$\left(\tan^{2}{\left(x \right)} + 1\right) \left. \frac{\partial}{\partial \xi_{2}} \frac{\log{\left(\sin{\left(x \right)} \right)}}{\log{\left(\xi_{2} \right)}} \right|_{\substack{ \xi_{2}=\tan{\left(x \right)} }} + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$$
Упростить
Вторая производная [src]
                                                                                       /           /       2   \ /         2     \            \
                                                                                       |           \1 + tan (x)/*|1 + -----------|*log(sin(x))|
                                                                         /       2   \ |  cos(x)                 \    log(tan(x))/            |
        2                                                                \1 + tan (x)/*|- ------ + -------------------------------------------|
     cos (x)     /       2   \ /  d  /log(sin(x))\\|                                   \  sin(x)                      tan(x)                  /
-1 - ------- + 2*\1 + tan (x)/*|-----|-----------|||           *tan(x) + ----------------------------------------------------------------------
        2                      \dxi_2\ log(xi_2) //|xi_2=tan(x)                                      2                                         
     sin (x)                                                                                      log (tan(x))*tan(x)
$$\frac{\left(\frac{\left(1 + \frac{2}{\log{\left(\tan{\left(x \right)} \right)}}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\sin{\left(x \right)} \right)}}{\tan{\left(x \right)}} - \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\log{\left(\tan{\left(x \right)} \right)}^{2} \tan{\left(x \right)}} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} \left. \frac{\partial}{\partial \xi_{2}} \frac{\log{\left(\sin{\left(x \right)} \right)}}{\log{\left(\xi_{2} \right)}} \right|_{\substack{ \xi_{2}=\tan{\left(x \right)} }} - 1 - \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}$$
Упростить
Третья производная [src]
                                                                                                                                                                                                                               /                                                                                                                                   2                                                                                         2                                                          \
                                                                                                                                                                                                                               |                                                                                                    2                 /       2   \  /         2     \               /       2   \ /         2     \            /       2   \  /         2     \                                        |
                                                                                           /           /       2   \ /         2     \            \                                                                            |       2                                                      /       2   \            /       2   \                2*\1 + tan (x)/ *|1 + -----------|*log(sin(x))   \1 + tan (x)/*|1 + -----------|*cos(x)   2*\1 + tan (x)/ *|1 + -----------|*log(sin(x))       /       2   \        |
                                                                                           |           \1 + tan (x)/*|1 + -----------|*log(sin(x))|                                                              /       2   \ |    cos (x)     /       2   \ /         2     \               \1 + tan (x)/*cos(x)   2*\1 + tan (x)/ *log(sin(x))                    \    log(tan(x))/                             \    log(tan(x))/                           \    log(tan(x))/                 2*\1 + tan (x)/*cos(x) |
                                                                             /       2   \ |  cos(x)                 \    log(tan(x))/            |                                                              \1 + tan (x)/*|1 + ------- + 2*\1 + tan (x)/*|1 + -----------|*log(sin(x)) + -------------------- - ---------------------------- - ---------------------------------------------- + -------------------------------------- - ---------------------------------------------- + -------------------------|
               2                                         3                 4*\1 + tan (x)/*|- ------ + -------------------------------------------|                                                                            |       2                      \    log(tan(x))/                  sin(x)*tan(x)              2            2                                2                                      sin(x)*tan(x)                                            2                    log(tan(x))*sin(x)*tan(x)|
  /       2   \  /  d  /log(sin(x))\\|              2*cos (x)   2*cos(x)                   \  sin(x)                      tan(x)                  /        2    /       2   \ /  d  /log(sin(x))\\|                            \    sin (x)                                                                              log (tan(x))*tan (x)                          tan (x)                                                                             log(tan(x))*tan (x)                                          /
2*\1 + tan (x)/ *|-----|-----------|||            + --------- + -------- + ------------------------------------------------------------------------ + 4*tan (x)*\1 + tan (x)/*|-----|-----------|||            + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                 \dxi_2\ log(xi_2) //|xi_2=tan(x)       3        sin(x)                                     2                                                                 \dxi_2\ log(xi_2) //|xi_2=tan(x)                                                                                                                                                2                                                                                                                                                          
                                                     sin (x)                                             log (tan(x))                                                                                                                                                                                                                                      log (tan(x))*tan(x)
$$\frac{4 \left(\frac{\left(1 + \frac{2}{\log{\left(\tan{\left(x \right)} \right)}}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\sin{\left(x \right)} \right)}}{\tan{\left(x \right)}} - \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\log{\left(\tan{\left(x \right)} \right)}^{2}} + 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \left. \frac{\partial}{\partial \xi_{2}} \frac{\log{\left(\sin{\left(x \right)} \right)}}{\log{\left(\xi_{2} \right)}} \right|_{\substack{ \xi_{2}=\tan{\left(x \right)} }} + \frac{\left(\tan^{2}{\left(x \right)} + 1\right) \left(- \frac{2 \cdot \left(1 + \frac{2}{\log{\left(\tan{\left(x \right)} \right)}}\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(\sin{\left(x \right)} \right)}}{\tan^{2}{\left(x \right)}} - \frac{2 \cdot \left(1 + \frac{2}{\log{\left(\tan{\left(x \right)} \right)}}\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(\sin{\left(x \right)} \right)}}{\log{\left(\tan{\left(x \right)} \right)} \tan^{2}{\left(x \right)}} + 2 \cdot \left(1 + \frac{2}{\log{\left(\tan{\left(x \right)} \right)}}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\sin{\left(x \right)} \right)} + \frac{\left(1 + \frac{2}{\log{\left(\tan{\left(x \right)} \right)}}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)}}{\sin{\left(x \right)} \tan{\left(x \right)}} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(\sin{\left(x \right)} \right)}}{\log{\left(\tan{\left(x \right)} \right)}^{2} \tan^{2}{\left(x \right)}} + \frac{\left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)}}{\sin{\left(x \right)} \tan{\left(x \right)}} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)}}{\log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)} \tan{\left(x \right)}} + 1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right)}{\log{\left(\tan{\left(x \right)} \right)}^{2} \tan{\left(x \right)}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} \left. \frac{\partial}{\partial \xi_{2}} \frac{\log{\left(\sin{\left(x \right)} \right)}}{\log{\left(\xi_{2} \right)}} \right|_{\substack{ \xi_{2}=\tan{\left(x \right)} }} + \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}}$$
Упростить
График
Производная log(sin(x),tan(x)) /media/krcore-image-pods/hash/derivative/e/39/e30823eeb8ad5bd28712dd749125f.png