Производная x^4*acot(x)
Решение
Вы ввели
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4 x *acot(x)
$$x^{4} \operatorname{acot}{\left (x \right )}$$
График
Первая производная
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4
x 3
- ------ + 4*x *acot(x)
2
1 + x
$$- \frac{x^{4}}{x^{2} + 1} + 4 x^{3} \operatorname{acot}{\left (x \right )}$$
Вторая производная
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/ 3 \
2 | x 4*x |
2*x *|6*acot(x) + --------- - ------|
| 2 2|
| / 2\ 1 + x |
\ \1 + x / /
$$2 x^{2} \left(\frac{x^{3}}{\left(x^{2} + 1\right)^{2}} - \frac{4 x}{x^{2} + 1} + 6 \operatorname{acot}{\left (x \right )}\right)$$
Третья производная
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/ 5 3 \
| 18*x 4*x 13*x |
2*x*|12*acot(x) - ------ - --------- + ---------|
| 2 3 2|
| 1 + x / 2\ / 2\ |
\ \1 + x / \1 + x / /
$$2 x \left(- \frac{4 x^{5}}{\left(x^{2} + 1\right)^{3}} + \frac{13 x^{3}}{\left(x^{2} + 1\right)^{2}} - \frac{18 x}{x^{2} + 1} + 12 \operatorname{acot}{\left (x \right )}\right)$$