Производная (asin(cos(x)))^atan(x)

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    atan(x)         |/log(asin(cos(x)))           atan(x)*sin(x)       \    2*x*log(asin(cos(x)))         sin (x)*atan(x)                  atan(x)*cos(x)                         2*sin(x)                      sin (x)*atan(x)*cos(x)   |
asin       (cos(x))*||----------------- - -----------------------------|  - --------------------- + ---------------------------- - ----------------------------- - -------------------------------------- + -----------------------------|
                    ||           2           _____________             |                  2         /        2   \     2              _____________                            _____________                             3/2             |
                    ||      1 + x           /        2                 |          /     2\          \-1 + cos (x)/*asin (cos(x))     /        2                    /     2\   /        2                    /       2   \                |
                    \\                    \/  1 - cos (x) *asin(cos(x))/          \1 + x /                                         \/  1 - cos (x) *asin(cos(x))   \1 + x /*\/  1 - cos (x) *asin(cos(x))   \1 - cos (x)/   *asin(cos(x))/

$$\left(\left(\frac{\log{\left(\operatorname{asin}{\left(\cos{\left(x \right)} \right)} \right)}}{x^{2} + 1} - \frac{\sin{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\sqrt{- \cos^{2}{\left(x \right)} + 1} \operatorname{asin}{\left(\cos{\left(x \right)} \right)}}\right)^{2} - \frac{2 x \log{\left(\operatorname{asin}{\left(\cos{\left(x \right)} \right)} \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{\sin^{2}{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\left(\cos^{2}{\left(x \right)} - 1\right) \operatorname{asin}^{2}{\left(\cos{\left(x \right)} \right)}} - \frac{\cos{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\sqrt{- \cos^{2}{\left(x \right)} + 1} \operatorname{asin}{\left(\cos{\left(x \right)} \right)}} + \frac{\sin^{2}{\left(x \right)} \cos{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\left(- \cos^{2}{\left(x \right)} + 1\right)^{\frac{3}{2}} \operatorname{asin}{\left(\cos{\left(x \right)} \right)}} - \frac{2 \sin{\left(x \right)}}{\sqrt{- \cos^{2}{\left(x \right)} + 1} \left(x^{2} + 1\right) \operatorname{asin}{\left(\cos{\left(x \right)} \right)}}\right) \operatorname{asin}^{\operatorname{atan}{\left(x \right)}}{\left(\cos{\left(x \right)} \right)}$$

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    atan(x)         |/log(asin(cos(x)))           atan(x)*sin(x)       \      /log(asin(cos(x)))           atan(x)*sin(x)       \ |2*x*log(asin(cos(x)))           atan(x)*cos(x)                sin (x)*atan(x)                         2*sin(x)                      sin (x)*atan(x)*cos(x)   |   2*log(asin(cos(x)))   8*x *log(asin(cos(x)))           atan(x)*sin(x)                 sin (x)*atan(x)                         3*cos(x)                        2*sin (x)*atan(x)                        3*sin (x)                   3*cos (x)*sin (x)*atan(x)                3*sin (x)*cos(x)                 3*cos (x)*atan(x)*sin(x)       3*atan(x)*cos(x)*sin(x)         3*sin (x)*atan(x)*cos(x)                    6*x*sin(x)              |
asin       (cos(x))*||----------------- - -----------------------------|  - 3*|----------------- - -----------------------------|*|--------------------- + ----------------------------- - ---------------------------- + -------------------------------------- - -----------------------------| - ------------------- + ---------------------- + ----------------------------- - ----------------------------- - -------------------------------------- - ------------------------------ + ------------------------------------- - ----------------------------- + -------------------------------------- + ----------------------------- + ---------------------------- + ----------------------------- + ---------------------------------------|
                    ||           2           _____________             |      |           2           _____________             | |              2            _____________                /        2   \     2                       _____________                             3/2             |                2                      3             _____________                             3/2                            _____________                             3/2                 /     2\ /        2   \     2                        5/2                                      3/2                             3/2                /        2   \     2                         2                         2    _____________             |
                    ||      1 + x           /        2                 |      |      1 + x           /        2                 | |      /     2\            /        2                    \-1 + cos (x)/*asin (cos(x))   /     2\   /        2                    /       2   \                |        /     2\               /     2\             /        2                    /       2   \                   /     2\   /        2                    /       2   \        3           \1 + x /*\-1 + cos (x)/*asin (cos(x))   /       2   \                   /     2\ /       2   \                   /       2   \                   \-1 + cos (x)/*asin (cos(x))   /        2   \      2           /     2\    /        2                 |
                    \\                    \/  1 - cos (x) *asin(cos(x))/      \                    \/  1 - cos (x) *asin(cos(x))/ \      \1 + x /          \/  1 - cos (x) *asin(cos(x))                                  \1 + x /*\/  1 - cos (x) *asin(cos(x))   \1 - cos (x)/   *asin(cos(x))/        \1 + x /               \1 + x /           \/  1 - cos (x) *asin(cos(x))   \1 - cos (x)/   *asin(cos(x))   \1 + x /*\/  1 - cos (x) *asin(cos(x))   \1 - cos (x)/   *asin (cos(x))                                           \1 - cos (x)/   *asin(cos(x))   \1 + x /*\1 - cos (x)/   *asin(cos(x))   \1 - cos (x)/   *asin(cos(x))                                  \-1 + cos (x)/ *asin (cos(x))   \1 + x / *\/  1 - cos (x) *asin(cos(x))/

$$\left(\left(\frac{\log{\left(\operatorname{asin}{\left(\cos{\left(x \right)} \right)} \right)}}{x^{2} + 1} - \frac{\sin{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\sqrt{- \cos^{2}{\left(x \right)} + 1} \operatorname{asin}{\left(\cos{\left(x \right)} \right)}}\right)^{3} - 3 \left(\frac{\log{\left(\operatorname{asin}{\left(\cos{\left(x \right)} \right)} \right)}}{x^{2} + 1} - \frac{\sin{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\sqrt{- \cos^{2}{\left(x \right)} + 1} \operatorname{asin}{\left(\cos{\left(x \right)} \right)}}\right) \left(\frac{2 x \log{\left(\operatorname{asin}{\left(\cos{\left(x \right)} \right)} \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{\sin^{2}{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\left(\cos^{2}{\left(x \right)} - 1\right) \operatorname{asin}^{2}{\left(\cos{\left(x \right)} \right)}} + \frac{\cos{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\sqrt{- \cos^{2}{\left(x \right)} + 1} \operatorname{asin}{\left(\cos{\left(x \right)} \right)}} - \frac{\sin^{2}{\left(x \right)} \cos{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\left(- \cos^{2}{\left(x \right)} + 1\right)^{\frac{3}{2}} \operatorname{asin}{\left(\cos{\left(x \right)} \right)}} + \frac{2 \sin{\left(x \right)}}{\sqrt{- \cos^{2}{\left(x \right)} + 1} \left(x^{2} + 1\right) \operatorname{asin}{\left(\cos{\left(x \right)} \right)}}\right) + \frac{3 \sin^{3}{\left(x \right)} \cos{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\left(\cos^{2}{\left(x \right)} - 1\right)^{2} \operatorname{asin}^{2}{\left(\cos{\left(x \right)} \right)}} + \frac{8 x^{2} \log{\left(\operatorname{asin}{\left(\cos{\left(x \right)} \right)} \right)}}{\left(x^{2} + 1\right)^{3}} + \frac{3 \sin{\left(x \right)} \cos{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\left(\cos^{2}{\left(x \right)} - 1\right) \operatorname{asin}^{2}{\left(\cos{\left(x \right)} \right)}} + \frac{\sin{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\sqrt{- \cos^{2}{\left(x \right)} + 1} \operatorname{asin}{\left(\cos{\left(x \right)} \right)}} - \frac{\sin^{3}{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\left(- \cos^{2}{\left(x \right)} + 1\right)^{\frac{3}{2}} \operatorname{asin}{\left(\cos{\left(x \right)} \right)}} + \frac{3 \sin{\left(x \right)} \cos^{2}{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\left(- \cos^{2}{\left(x \right)} + 1\right)^{\frac{3}{2}} \operatorname{asin}{\left(\cos{\left(x \right)} \right)}} - \frac{3 \sin^{3}{\left(x \right)} \cos^{2}{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\left(- \cos^{2}{\left(x \right)} + 1\right)^{\frac{5}{2}} \operatorname{asin}{\left(\cos{\left(x \right)} \right)}} - \frac{2 \log{\left(\operatorname{asin}{\left(\cos{\left(x \right)} \right)} \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{6 x \sin{\left(x \right)}}{\sqrt{- \cos^{2}{\left(x \right)} + 1} \left(x^{2} + 1\right)^{2} \operatorname{asin}{\left(\cos{\left(x \right)} \right)}} + \frac{3 \sin^{2}{\left(x \right)}}{\left(x^{2} + 1\right) \left(\cos^{2}{\left(x \right)} - 1\right) \operatorname{asin}^{2}{\left(\cos{\left(x \right)} \right)}} - \frac{3 \cos{\left(x \right)}}{\sqrt{- \cos^{2}{\left(x \right)} + 1} \left(x^{2} + 1\right) \operatorname{asin}{\left(\cos{\left(x \right)} \right)}} - \frac{2 \sin^{3}{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\left(- \cos^{2}{\left(x \right)} + 1\right)^{\frac{3}{2}} \operatorname{asin}^{3}{\left(\cos{\left(x \right)} \right)}} + \frac{3 \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{\left(- \cos^{2}{\left(x \right)} + 1\right)^{\frac{3}{2}} \left(x^{2} + 1\right) \operatorname{asin}{\left(\cos{\left(x \right)} \right)}}\right) \operatorname{asin}^{\operatorname{atan}{\left(x \right)}}{\left(\cos{\left(x \right)} \right)}$$

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