Подробное решение
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Не могу найти шаги в поиске этой производной.
Но производная
Ответ:
3
sin (3*x) / 3 \
/ /4 ___\\ | 2 / /4 ___\\ sin (3*x) |
\atan\\/ x // *|9*sin (3*x)*cos(3*x)*log\atan\\/ x // + ------------------------------|
| 3/4 / ___\ /4 ___\|
\ 4*x *\1 + \/ x /*atan\\/ x //
$$\left(9 \log{\left(\operatorname{atan}{\left(\sqrt[4]{x} \right)} \right)} \sin^{2}{\left(3 x \right)} \cos{\left(3 x \right)} + \frac{\sin^{3}{\left(3 x \right)}}{4 x^{\frac{3}{4}} \left(\sqrt{x} + 1\right) \operatorname{atan}{\left(\sqrt[4]{x} \right)}}\right) \operatorname{atan}^{\sin^{3}{\left(3 x \right)}}{\left(\sqrt[4]{x} \right)}$$
/ 2 \
| / / /4 ___\\ sin(3*x) \ 3 |
3 | |36*cos(3*x)*log\atan\\/ x // + ----------------------------| *sin (3*x) |
sin (3*x) | | 3/4 / ___\ /4 ___\| 2 2 2 |
/ /4 ___\\ | 2 / /4 ___\\ 2 / /4 ___\\ \ x *\1 + \/ x /*atan\\/ x // 3*sin (3*x) sin (3*x) sin (3*x) 9*cos(3*x)*sin(3*x) |
\atan\\/ x // *|- 27*sin (3*x)*log\atan\\/ x // + 54*cos (3*x)*log\atan\\/ x // + ------------------------------------------------------------------------ - ------------------------------- - ------------------------------- - --------------------------------- + ------------------------------|*sin(3*x)
| 16 7/4 / ___\ /4 ___\ 2 2 3/4 / ___\ /4 ___\|
| 16*x *\1 + \/ x /*atan\\/ x / 5/4 / ___\ /4 ___\ 3/2 / ___\ 2/4 ___\ 2*x *\1 + \/ x /*atan\\/ x /|
\ 8*x *\1 + \/ x / *atan\\/ x / 16*x *\1 + \/ x / *atan \\/ x / /
$$\left(\frac{\left(36 \log{\left(\operatorname{atan}{\left(\sqrt[4]{x} \right)} \right)} \cos{\left(3 x \right)} + \frac{\sin{\left(3 x \right)}}{x^{\frac{3}{4}} \left(\sqrt{x} + 1\right) \operatorname{atan}{\left(\sqrt[4]{x} \right)}}\right)^{2} \sin^{3}{\left(3 x \right)}}{16} - 27 \log{\left(\operatorname{atan}{\left(\sqrt[4]{x} \right)} \right)} \sin^{2}{\left(3 x \right)} + 54 \log{\left(\operatorname{atan}{\left(\sqrt[4]{x} \right)} \right)} \cos^{2}{\left(3 x \right)} + \frac{9 \sin{\left(3 x \right)} \cos{\left(3 x \right)}}{2 x^{\frac{3}{4}} \left(\sqrt{x} + 1\right) \operatorname{atan}{\left(\sqrt[4]{x} \right)}} - \frac{\sin^{2}{\left(3 x \right)}}{16 x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)^{2} \operatorname{atan}^{2}{\left(\sqrt[4]{x} \right)}} - \frac{\sin^{2}{\left(3 x \right)}}{8 x^{\frac{5}{4}} \left(\sqrt{x} + 1\right)^{2} \operatorname{atan}{\left(\sqrt[4]{x} \right)}} - \frac{3 \sin^{2}{\left(3 x \right)}}{16 x^{\frac{7}{4}} \left(\sqrt{x} + 1\right) \operatorname{atan}{\left(\sqrt[4]{x} \right)}}\right) \sin{\left(3 x \right)} \operatorname{atan}^{\sin^{3}{\left(3 x \right)}}{\left(\sqrt[4]{x} \right)}$$
/ / 2 2 2 \ \
| 3 3 / / /4 ___\\ sin(3*x) \ | 2 / /4 ___\\ 2 / /4 ___\\ sin (3*x) 2*sin (3*x) 3*sin (3*x) 72*cos(3*x)*sin(3*x) | |
| / / /4 ___\\ sin(3*x) \ 6 3*sin (3*x)*|36*cos(3*x)*log\atan\\/ x // + ----------------------------|*|- 864*cos (3*x)*log\atan\\/ x // + 432*sin (3*x)*log\atan\\/ x // + ------------------------------ + ----------------------------- + ---------------------------- - ----------------------------| |
3 | |36*cos(3*x)*log\atan\\/ x // + ----------------------------| *sin (3*x) | 3/4 / ___\ /4 ___\| | 2 2 7/4 / ___\ /4 ___\ 3/4 / ___\ /4 ___\| |
sin (3*x) | | 3/4 / ___\ /4 ___\| \ x *\1 + \/ x /*atan\\/ x // | 3/2 / ___\ 2/4 ___\ 5/4 / ___\ /4 ___\ x *\1 + \/ x /*atan\\/ x / x *\1 + \/ x /*atan\\/ x /| 3 3 3 3 3 3 3 2 2 2 2 |
/ /4 ___\\ | 3 / /4 ___\\ \ x *\1 + \/ x /*atan\\/ x // 2 / /4 ___\\ \ x *\1 + \/ x / *atan \\/ x / x *\1 + \/ x / *atan\\/ x / / 81*sin (3*x) sin (3*x) sin (3*x) sin (3*x) 3*sin (3*x) 9*sin (3*x) 21*sin (3*x) 81*sin (3*x)*cos(3*x) 27*sin (3*x)*cos(3*x) 27*sin (3*x)*cos(3*x) 81*cos (3*x)*sin(3*x) |
\atan\\/ x // *|162*cos (3*x)*log\atan\\/ x // + ------------------------------------------------------------------------ - 567*sin (3*x)*cos(3*x)*log\atan\\/ x // - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------ + ------------------------------- + ------------------------------- + --------------------------------- + ------------------------------- + --------------------------------- + -------------------------------- - ------------------------------- - ------------------------------- - --------------------------------- + ------------------------------|
| 64 64 3/4 / ___\ /4 ___\ 2 3 3 3 2 11/4 / ___\ /4 ___\ 7/4 / ___\ /4 ___\ 2 2 3/4 / ___\ /4 ___\|
| 4*x *\1 + \/ x /*atan\\/ x / 9/4 / ___\ /4 ___\ 7/4 / ___\ /4 ___\ 9/4 / ___\ 3/4 ___\ 2 / ___\ 2/4 ___\ 5/2 / ___\ 2/4 ___\ 64*x *\1 + \/ x /*atan\\/ x / 16*x *\1 + \/ x /*atan\\/ x / 5/4 / ___\ /4 ___\ 3/2 / ___\ 2/4 ___\ 2*x *\1 + \/ x /*atan\\/ x /|
\ 4*x *\1 + \/ x / *atan\\/ x / 8*x *\1 + \/ x / *atan\\/ x / 32*x *\1 + \/ x / *atan \\/ x / 32*x *\1 + \/ x / *atan \\/ x / 64*x *\1 + \/ x / *atan \\/ x / 8*x *\1 + \/ x / *atan\\/ x / 16*x *\1 + \/ x / *atan \\/ x / /
$$\left(\frac{\left(36 \log{\left(\operatorname{atan}{\left(\sqrt[4]{x} \right)} \right)} \cos{\left(3 x \right)} + \frac{\sin{\left(3 x \right)}}{x^{\frac{3}{4}} \left(\sqrt{x} + 1\right) \operatorname{atan}{\left(\sqrt[4]{x} \right)}}\right)^{3} \sin^{6}{\left(3 x \right)}}{64} - \frac{3 \cdot \left(36 \log{\left(\operatorname{atan}{\left(\sqrt[4]{x} \right)} \right)} \cos{\left(3 x \right)} + \frac{\sin{\left(3 x \right)}}{x^{\frac{3}{4}} \left(\sqrt{x} + 1\right) \operatorname{atan}{\left(\sqrt[4]{x} \right)}}\right) \left(432 \log{\left(\operatorname{atan}{\left(\sqrt[4]{x} \right)} \right)} \sin^{2}{\left(3 x \right)} - 864 \log{\left(\operatorname{atan}{\left(\sqrt[4]{x} \right)} \right)} \cos^{2}{\left(3 x \right)} - \frac{72 \sin{\left(3 x \right)} \cos{\left(3 x \right)}}{x^{\frac{3}{4}} \left(\sqrt{x} + 1\right) \operatorname{atan}{\left(\sqrt[4]{x} \right)}} + \frac{\sin^{2}{\left(3 x \right)}}{x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)^{2} \operatorname{atan}^{2}{\left(\sqrt[4]{x} \right)}} + \frac{2 \sin^{2}{\left(3 x \right)}}{x^{\frac{5}{4}} \left(\sqrt{x} + 1\right)^{2} \operatorname{atan}{\left(\sqrt[4]{x} \right)}} + \frac{3 \sin^{2}{\left(3 x \right)}}{x^{\frac{7}{4}} \left(\sqrt{x} + 1\right) \operatorname{atan}{\left(\sqrt[4]{x} \right)}}\right) \sin^{3}{\left(3 x \right)}}{64} - 567 \log{\left(\operatorname{atan}{\left(\sqrt[4]{x} \right)} \right)} \sin^{2}{\left(3 x \right)} \cos{\left(3 x \right)} + 162 \log{\left(\operatorname{atan}{\left(\sqrt[4]{x} \right)} \right)} \cos^{3}{\left(3 x \right)} - \frac{81 \sin^{3}{\left(3 x \right)}}{4 x^{\frac{3}{4}} \left(\sqrt{x} + 1\right) \operatorname{atan}{\left(\sqrt[4]{x} \right)}} + \frac{81 \sin{\left(3 x \right)} \cos^{2}{\left(3 x \right)}}{2 x^{\frac{3}{4}} \left(\sqrt{x} + 1\right) \operatorname{atan}{\left(\sqrt[4]{x} \right)}} + \frac{3 \sin^{3}{\left(3 x \right)}}{32 x^{2} \left(\sqrt{x} + 1\right)^{3} \operatorname{atan}^{2}{\left(\sqrt[4]{x} \right)}} - \frac{27 \sin^{2}{\left(3 x \right)} \cos{\left(3 x \right)}}{16 x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)^{2} \operatorname{atan}^{2}{\left(\sqrt[4]{x} \right)}} - \frac{27 \sin^{2}{\left(3 x \right)} \cos{\left(3 x \right)}}{8 x^{\frac{5}{4}} \left(\sqrt{x} + 1\right)^{2} \operatorname{atan}{\left(\sqrt[4]{x} \right)}} + \frac{9 \sin^{3}{\left(3 x \right)}}{64 x^{\frac{5}{2}} \left(\sqrt{x} + 1\right)^{2} \operatorname{atan}^{2}{\left(\sqrt[4]{x} \right)}} - \frac{81 \sin^{2}{\left(3 x \right)} \cos{\left(3 x \right)}}{16 x^{\frac{7}{4}} \left(\sqrt{x} + 1\right) \operatorname{atan}{\left(\sqrt[4]{x} \right)}} + \frac{\sin^{3}{\left(3 x \right)}}{8 x^{\frac{7}{4}} \left(\sqrt{x} + 1\right)^{3} \operatorname{atan}{\left(\sqrt[4]{x} \right)}} + \frac{\sin^{3}{\left(3 x \right)}}{4 x^{\frac{9}{4}} \left(\sqrt{x} + 1\right)^{2} \operatorname{atan}{\left(\sqrt[4]{x} \right)}} + \frac{21 \sin^{3}{\left(3 x \right)}}{64 x^{\frac{11}{4}} \left(\sqrt{x} + 1\right) \operatorname{atan}{\left(\sqrt[4]{x} \right)}} + \frac{\sin^{3}{\left(3 x \right)}}{32 x^{\frac{9}{4}} \left(\sqrt{x} + 1\right)^{3} \operatorname{atan}^{3}{\left(\sqrt[4]{x} \right)}}\right) \operatorname{atan}^{\sin^{3}{\left(3 x \right)}}{\left(\sqrt[4]{x} \right)}$$