Дано
$$left(x^{3} cot{left (2 right )}right)^{sin{left (sqrt{x} right )}}$$
Подробное решение
-
Не могу найти шаги в поиске этой производной.
Но производная
left(log{left (sin{left (sqrt{x} right )} right )} + 1right) sin^{sin{left (sqrt{x} right )}}{left (sqrt{x} right )}
Ответ:
left(log{left (sin{left (sqrt{x} right )} right )} + 1right) sin^{sin{left (sqrt{x} right )}}{left (sqrt{x} right )}
Первая производная
/ ___
sin/ x / / / ___ / ___ / 3
/ 3 |3*sin/ x / cos/ x /*logcot(2)*x /|
cot(2)*x / *|———— + ————————-|
| x ___ |
2*/ x /
$$left(x^{3} cot{left (2 right )}right)^{sin{left (sqrt{x} right )}} left(frac{3}{x} sin{left (sqrt{x} right )} + frac{cos{left (sqrt{x} right )}}{2 sqrt{x}} log{left (x^{3} cot{left (2 right )} right )}right)$$
Вторая производная
/ 2
|/ / ___ / ___ / 3 |
||6*sin/ x / cos/ x /*logx *cot(2)/| |
/ ___ ||———— + ————————-| |
sin/ x / || x ___ | / ___ / ___ / 3 / ___ / ___ / 3 |
/ 3 | / x / 3*sin/ x / 3*cos/ x / logx *cot(2)/*sin/ x / cos/ x /*logx *cot(2)/|
x *cot(2)/ *|——————————————- – ———— + ———— – ————————- – ————————-|
| 4 2 3/2 4*x 3/2 |
x x 4*x /
$$left(x^{3} cot{left (2 right )}right)^{sin{left (sqrt{x} right )}} left(frac{1}{4} left(frac{6}{x} sin{left (sqrt{x} right )} + frac{1}{sqrt{x}} log{left (x^{3} cot{left (2 right )} right )} cos{left (sqrt{x} right )}right)^{2} – frac{sin{left (sqrt{x} right )}}{4 x} log{left (x^{3} cot{left (2 right )} right )} – frac{3}{x^{2}} sin{left (sqrt{x} right )} – frac{cos{left (sqrt{x} right )}}{4 x^{frac{3}{2}}} log{left (x^{3} cot{left (2 right )} right )} + frac{3}{x^{frac{3}{2}}} cos{left (sqrt{x} right )}right)$$
Третья производная
/ 3
|/ / ___ / ___ / 3 / / ___ / ___ / 3 / / ___ / ___ / 3 / ___ / ___ / 3 |
||6*sin/ x / cos/ x /*logx *cot(2)/| |6*sin/ x / cos/ x /*logx *cot(2)/| | 12*cos/ x / 12*sin/ x / logx *cot(2)/*sin/ x / cos/ x /*logx *cot(2)/| |
/ ___ ||———— + ————————-| 3*|———— + ————————-|*|- ————- + ————- + ————————- + ————————-| |
sin/ x / || x ___ | / ___ / ___ / ___ | x ___ | | 3/2 2 x 3/2 | / ___ / 3 / 3 / ___ / ___ / 3 |
/ 3 | / x / 6*sin/ x / 27*cos/ x / 9*sin/ x / / x / x x x / cos/ x /*logx *cot(2)/ 3*logx *cot(2)/*sin/ x / 3*cos/ x /*logx *cot(2)/|
x *cot(2)/ *|——————————————- + ———— – ————- – ———— – ————————————————————————————————————————————– – ————————- + ————————— + —————————|
| 8 3 5/2 2 8 3/2 2 5/2 |
x 4*x 4*x 8*x 8*x 8*x /
$$left(x^{3} cot{left (2 right )}right)^{sin{left (sqrt{x} right )}} left(frac{1}{8} left(frac{6}{x} sin{left (sqrt{x} right )} + frac{1}{sqrt{x}} log{left (x^{3} cot{left (2 right )} right )} cos{left (sqrt{x} right )}right)^{3} – frac{3}{8} left(frac{6}{x} sin{left (sqrt{x} right )} + frac{1}{sqrt{x}} log{left (x^{3} cot{left (2 right )} right )} cos{left (sqrt{x} right )}right) left(frac{1}{x} log{left (x^{3} cot{left (2 right )} right )} sin{left (sqrt{x} right )} + frac{12}{x^{2}} sin{left (sqrt{x} right )} + frac{1}{x^{frac{3}{2}}} log{left (x^{3} cot{left (2 right )} right )} cos{left (sqrt{x} right )} – frac{12}{x^{frac{3}{2}}} cos{left (sqrt{x} right )}right) + frac{3}{8 x^{2}} log{left (x^{3} cot{left (2 right )} right )} sin{left (sqrt{x} right )} – frac{9}{4 x^{2}} sin{left (sqrt{x} right )} + frac{6}{x^{3}} sin{left (sqrt{x} right )} – frac{cos{left (sqrt{x} right )}}{8 x^{frac{3}{2}}} log{left (x^{3} cot{left (2 right )} right )} + frac{3}{8 x^{frac{5}{2}}} log{left (x^{3} cot{left (2 right )} right )} cos{left (sqrt{x} right )} – frac{27}{4 x^{frac{5}{2}}} cos{left (sqrt{x} right )}right)$$
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