Производная (sin(x)+x^2)^(cos(x))
Решение
Вы ввели
[TeX]
[pretty]
[text]
cos(x) / 2\ \sin(x) + x /
$$\left(x^{2} + \sin{\left (x \right )}\right)^{\cos{\left (x \right )}}$$
Подробное решение
[TeX]
Не могу найти шаги в поиске этой производной.
Но производная
Ответ:
График
Первая производная
[TeX]
[pretty]
[text]
cos(x)
/ 2\ / / 2\ (2*x + cos(x))*cos(x)\
\sin(x) + x / *|- log\sin(x) + x /*sin(x) + ---------------------|
| 2 |
\ sin(x) + x /
$$\left(x^{2} + \sin{\left (x \right )}\right)^{\cos{\left (x \right )}} \left(\frac{\left(2 x + \cos{\left (x \right )}\right) \cos{\left (x \right )}}{x^{2} + \sin{\left (x \right )}} - \log{\left (x^{2} + \sin{\left (x \right )} \right )} \sin{\left (x \right )}\right)$$
Вторая производная
[TeX]
[pretty]
[text]
cos(x) / 2 2 \
/ 2 \ |/ / 2 \ (2*x + cos(x))*cos(x)\ / 2 \ (-2 + sin(x))*cos(x) (2*x + cos(x)) *cos(x) 2*(2*x + cos(x))*sin(x)|
\x + sin(x)/ *||- log\x + sin(x)/*sin(x) + ---------------------| - cos(x)*log\x + sin(x)/ - -------------------- - ---------------------- - -----------------------|
|| 2 | 2 2 2 |
|\ x + sin(x) / x + sin(x) / 2 \ x + sin(x) |
\ \x + sin(x)/ /
$$\left(x^{2} + \sin{\left (x \right )}\right)^{\cos{\left (x \right )}} \left(- \frac{\left(2 x + \cos{\left (x \right )}\right)^{2} \cos{\left (x \right )}}{\left(x^{2} + \sin{\left (x \right )}\right)^{2}} - \frac{2 \left(2 x + \cos{\left (x \right )}\right) \sin{\left (x \right )}}{x^{2} + \sin{\left (x \right )}} + \left(\frac{\left(2 x + \cos{\left (x \right )}\right) \cos{\left (x \right )}}{x^{2} + \sin{\left (x \right )}} - \log{\left (x^{2} + \sin{\left (x \right )} \right )} \sin{\left (x \right )}\right)^{2} - \log{\left (x^{2} + \sin{\left (x \right )} \right )} \cos{\left (x \right )} - \frac{\left(\sin{\left (x \right )} - 2\right) \cos{\left (x \right )}}{x^{2} + \sin{\left (x \right )}}\right)$$
Третья производная
[TeX]
[pretty]
[text]
cos(x) / 3 2 / 2 \ 3 2 \
/ 2 \ |/ / 2 \ (2*x + cos(x))*cos(x)\ / 2 \ cos (x) / / 2 \ (2*x + cos(x))*cos(x)\ | / 2 \ (-2 + sin(x))*cos(x) (2*x + cos(x)) *cos(x) 2*(2*x + cos(x))*sin(x)| 3*(2*x + cos(x))*cos(x) 2*(2*x + cos(x)) *cos(x) 3*(-2 + sin(x))*sin(x) 3*(2*x + cos(x)) *sin(x) 3*(-2 + sin(x))*(2*x + cos(x))*cos(x)|
\x + sin(x)/ *||- log\x + sin(x)/*sin(x) + ---------------------| + log\x + sin(x)/*sin(x) - ----------- - 3*|- log\x + sin(x)/*sin(x) + ---------------------|*|cos(x)*log\x + sin(x)/ + -------------------- + ---------------------- + -----------------------| - ----------------------- + ------------------------ + ---------------------- + ------------------------ + -------------------------------------|
|| 2 | 2 | 2 | | 2 2 2 | 2 3 2 2 2 |
|\ x + sin(x) / x + sin(x) \ x + sin(x) / | x + sin(x) / 2 \ x + sin(x) | x + sin(x) / 2 \ x + sin(x) / 2 \ / 2 \ |
\ \ \x + sin(x)/ / \x + sin(x)/ \x + sin(x)/ \x + sin(x)/ /
$$\left(x^{2} + \sin{\left (x \right )}\right)^{\cos{\left (x \right )}} \left(\frac{2 \left(2 x + \cos{\left (x \right )}\right)^{3} \cos{\left (x \right )}}{\left(x^{2} + \sin{\left (x \right )}\right)^{3}} + \frac{3 \left(2 x + \cos{\left (x \right )}\right)^{2} \sin{\left (x \right )}}{\left(x^{2} + \sin{\left (x \right )}\right)^{2}} - \frac{3 \left(2 x + \cos{\left (x \right )}\right) \cos{\left (x \right )}}{x^{2} + \sin{\left (x \right )}} + \frac{3 \cos{\left (x \right )}}{\left(x^{2} + \sin{\left (x \right )}\right)^{2}} \left(2 x + \cos{\left (x \right )}\right) \left(\sin{\left (x \right )} - 2\right) + \left(\frac{\left(2 x + \cos{\left (x \right )}\right) \cos{\left (x \right )}}{x^{2} + \sin{\left (x \right )}} - \log{\left (x^{2} + \sin{\left (x \right )} \right )} \sin{\left (x \right )}\right)^{3} - 3 \left(\frac{\left(2 x + \cos{\left (x \right )}\right) \cos{\left (x \right )}}{x^{2} + \sin{\left (x \right )}} - \log{\left (x^{2} + \sin{\left (x \right )} \right )} \sin{\left (x \right )}\right) \left(\frac{\left(2 x + \cos{\left (x \right )}\right)^{2} \cos{\left (x \right )}}{\left(x^{2} + \sin{\left (x \right )}\right)^{2}} + \frac{2 \left(2 x + \cos{\left (x \right )}\right) \sin{\left (x \right )}}{x^{2} + \sin{\left (x \right )}} + \log{\left (x^{2} + \sin{\left (x \right )} \right )} \cos{\left (x \right )} + \frac{\left(\sin{\left (x \right )} - 2\right) \cos{\left (x \right )}}{x^{2} + \sin{\left (x \right )}}\right) + \log{\left (x^{2} + \sin{\left (x \right )} \right )} \sin{\left (x \right )} + \frac{3 \left(\sin{\left (x \right )} - 2\right) \sin{\left (x \right )}}{x^{2} + \sin{\left (x \right )}} - \frac{\cos^{2}{\left (x \right )}}{x^{2} + \sin{\left (x \right )}}\right)$$