Господин Экзамен

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atan(2*x^sin(x))
Производная функции/ atan(2*x^sin(x))

Производная atan(2*x^sin(x))

Функция f() - производная -го порядка в точке
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Решение

Вы ввели [src] 
    /   sin(x)\
atan\2*x      /
atan⁡(2xsin⁡(x))\operatorname{atan}{\left(2 x^{\sin{\left(x \right)}} \right)} 
d /    /   sin(x)\\
--\atan\2*x      //
dx
ddxatan⁡(2xsin⁡(x))\frac{d}{d x} \operatorname{atan}{\left(2 x^{\sin{\left(x \right)}} \right)}
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График
02468-8-6-4-2-10102.5-2.5
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Первая производная [src] 
   sin(x) /sin(x)                \
2*x      *|------ + cos(x)*log(x)|
          \  x                   /
----------------------------------
                2*sin(x)          
         1 + 4*x
2xsin⁡(x)(log⁡(x)cos⁡(x)+sin⁡(x)x)4x2sin⁡(x)+1\frac{2 x^{\sin{\left(x \right)}} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)}{4 x^{2 \sin{\left(x \right)}} + 1}
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Вторая производная [src] 
          /                                                                                                    2\
          |                                                                   2*sin(x) /sin(x)                \ |
          |                        2                                       8*x        *|------ + cos(x)*log(x)| |
   sin(x) |/sin(x)                \    sin(x)                   2*cos(x)               \  x                   / |
2*x      *||------ + cos(x)*log(x)|  - ------ - log(x)*sin(x) + -------- - -------------------------------------|
          |\  x                   /       2                        x                         2*sin(x)           |
          \                              x                                            1 + 4*x                   /
-----------------------------------------------------------------------------------------------------------------
                                                        2*sin(x)                                                 
                                                 1 + 4*x
2xsin⁡(x)(−8x2sin⁡(x)(log⁡(x)cos⁡(x)+sin⁡(x)x)24x2sin⁡(x)+1+(log⁡(x)cos⁡(x)+sin⁡(x)x)2−log⁡(x)sin⁡(x)+2cos⁡(x)x−sin⁡(x)x2)4x2sin⁡(x)+1\frac{2 x^{\sin{\left(x \right)}} \left(- \frac{8 x^{2 \sin{\left(x \right)}} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{2}}{4 x^{2 \sin{\left(x \right)}} + 1} + \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{2} - \log{\left(x \right)} \sin{\left(x \right)} + \frac{2 \cos{\left(x \right)}}{x} - \frac{\sin{\left(x \right)}}{x^{2}}\right)}{4 x^{2 \sin{\left(x \right)}} + 1}
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Третья производная [src] 
          /                                                                                                                                                                                   3                                         3       2*sin(x) /sin(x)                \ /sin(x)                   2*cos(x)\\
          |                                                                                                                                                  2*sin(x) /sin(x)                \         4*sin(x) /sin(x)                \    24*x        *|------ + cos(x)*log(x)|*|------ + log(x)*sin(x) - --------||
          |                        3                                                                                                                     32*x        *|------ + cos(x)*log(x)|    128*x        *|------ + cos(x)*log(x)|                 \  x                   / |   2                        x    ||
   sin(x) |/sin(x)                \                    3*sin(x)   3*cos(x)     /sin(x)                \ /sin(x)                   2*cos(x)\   2*sin(x)                \  x                   /                  \  x                   /                                          \  x                              /|
2*x      *||------ + cos(x)*log(x)|  - cos(x)*log(x) - -------- - -------- - 3*|------ + cos(x)*log(x)|*|------ + log(x)*sin(x) - --------| + -------- - -------------------------------------- + --------------------------------------- + -------------------------------------------------------------------------|
          |\  x                   /                       x           2        \  x                   / |   2                        x    |       3                        2*sin(x)                                           2                                                 2*sin(x)                             |
          |                                                          x                                  \  x                              /      x                  1 + 4*x                                  /       2*sin(x)\                                           1 + 4*x                                     |
          \                                                                                                                                                                                                  \1 + 4*x        /                                                                                       /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                          2*sin(x)                                                                                                                                                    
                                                                                                                                                   1 + 4*x
2xsin⁡(x)(128x4sin⁡(x)(log⁡(x)cos⁡(x)+sin⁡(x)x)3(4x2sin⁡(x)+1)2−32x2sin⁡(x)(log⁡(x)cos⁡(x)+sin⁡(x)x)34x2sin⁡(x)+1+24x2sin⁡(x)(log⁡(x)cos⁡(x)+sin⁡(x)x)(log⁡(x)sin⁡(x)−2cos⁡(x)x+sin⁡(x)x2)4x2sin⁡(x)+1+(log⁡(x)cos⁡(x)+sin⁡(x)x)3−3(log⁡(x)cos⁡(x)+sin⁡(x)x)(log⁡(x)sin⁡(x)−2cos⁡(x)x+sin⁡(x)x2)−log⁡(x)cos⁡(x)−3sin⁡(x)x−3cos⁡(x)x2+2sin⁡(x)x3)4x2sin⁡(x)+1\frac{2 x^{\sin{\left(x \right)}} \left(\frac{128 x^{4 \sin{\left(x \right)}} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{3}}{\left(4 x^{2 \sin{\left(x \right)}} + 1\right)^{2}} - \frac{32 x^{2 \sin{\left(x \right)}} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{3}}{4 x^{2 \sin{\left(x \right)}} + 1} + \frac{24 x^{2 \sin{\left(x \right)}} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{\sin{\left(x \right)}}{x^{2}}\right)}{4 x^{2 \sin{\left(x \right)}} + 1} + \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{3} - 3 \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{\sin{\left(x \right)}}{x^{2}}\right) - \log{\left(x \right)} \cos{\left(x \right)} - \frac{3 \sin{\left(x \right)}}{x} - \frac{3 \cos{\left(x \right)}}{x^{2}} + \frac{2 \sin{\left(x \right)}}{x^{3}}\right)}{4 x^{2 \sin{\left(x \right)}} + 1}
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Производная atan(2*x^sin(x))
    © Господин Экзамен – Калькулятор