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Производная asin(sin(x)-cos(x))

Функция f() - производная -го порядка в точке
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Кусочно-заданная:

Решение

Вы ввели [src]
asin(sin(x) - cos(x))
asin(sin(x)cos(x))\operatorname{asin}{\left(\sin{\left(x \right)} - \cos{\left(x \right)} \right)}
d                        
--(asin(sin(x) - cos(x)))
dx                       
ddxasin(sin(x)cos(x))\frac{d}{d x} \operatorname{asin}{\left(\sin{\left(x \right)} - \cos{\left(x \right)} \right)}
График
02468-8-6-4-2-1010-1010
Первая производная [src]
      cos(x) + sin(x)      
---------------------------
   ________________________
  /                      2 
\/  1 - (sin(x) - cos(x))  
sin(x)+cos(x)(sin(x)cos(x))2+1\frac{\sin{\left(x \right)} + \cos{\left(x \right)}}{\sqrt{- \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2} + 1}}
Вторая производная [src]
/                         2  \                   
|        (cos(x) + sin(x))   |                   
|-1 + -----------------------|*(-cos(x) + sin(x))
|                           2|                   
\     1 - (-cos(x) + sin(x)) /                   
-------------------------------------------------
              _________________________          
             /                       2           
           \/  1 - (-cos(x) + sin(x))            
((sin(x)+cos(x))2(sin(x)cos(x))2+11)(sin(x)cos(x))(sin(x)cos(x))2+1\frac{\left(\frac{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}}{- \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2} + 1} - 1\right) \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)}{\sqrt{- \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2} + 1}}
Третья производная [src]
                  /                         2                          2                        2                  2\
                  |        (cos(x) + sin(x))       3*(-cos(x) + sin(x))     3*(-cos(x) + sin(x)) *(cos(x) + sin(x)) |
(cos(x) + sin(x))*|-1 + ----------------------- - ----------------------- + ----------------------------------------|
                  |                           2                         2                                   2       |
                  |     1 - (-cos(x) + sin(x))    1 - (-cos(x) + sin(x))           /                      2\        |
                  \                                                                \1 - (-cos(x) + sin(x)) /        /
---------------------------------------------------------------------------------------------------------------------
                                                _________________________                                            
                                               /                       2                                             
                                             \/  1 - (-cos(x) + sin(x))                                              
(sin(x)+cos(x))(3(sin(x)cos(x))2(sin(x)+cos(x))2((sin(x)cos(x))2+1)23(sin(x)cos(x))2(sin(x)cos(x))2+1+(sin(x)+cos(x))2(sin(x)cos(x))2+11)(sin(x)cos(x))2+1\frac{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right) \left(\frac{3 \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2} \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}}{\left(- \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2} + 1\right)^{2}} - \frac{3 \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}}{- \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2} + 1} + \frac{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}}{- \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2} + 1} - 1\right)}{\sqrt{- \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2} + 1}}
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Производная asin(sin(x)-cos(x))