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