Задача 77849 ...
Условие
Решение
[m] y_1 = \cot(x) [/m]
Производная [m] \cot(x) [/m]:
[m] \frac{d}{dx}[\cot(x)] = -\csc^2(x) [/m]
2. Найдём производную [m] 6\sqrt{x} [/m].
[m] y_2 = 6\sqrt{x} = 6x^{1/2} [/m]
Производная [m] 6x^{1/2} [/m]:
[m] \frac{d}{dx}[6x^{1/2}] = 6 \cdot \frac{1}{2} x^{-1/2} = 3x^{-1/2} [/m]
или
[m] \frac{d}{dx}[6\sqrt{x}] = 3\sqrt{x^{-1}} = \frac{3}{\sqrt{x}} [/m]
3. Сложив произведённые производные, получаем:
[m] \frac{d}{dx}\left[\cot(x) + 6\sqrt{x}\right] = \frac{d}{dx}[\cot(x)] + \frac{d}{dx}[6\sqrt{x}] [/m]
[m] = -\csc^2(x) + \frac{3}{\sqrt{x}} [/m]
Ответ:
[m] \frac{d}{dx}\left[\cot(x) + 6\sqrt{x}\right] = -\csc^2(x) + \frac{3}{\sqrt{x}} [/m]
Все решения