Question

Найдите значение производной сложной функции в точке хо: ​

Answer 1

Ответ:

$f(x) = {tg}^{3} (5x)$

$f'(x) = 3 {tg}^{2} (5x) \times (tg(5x))' \times (5x)' = \\ = 3 {tg}^{2} (5x) \times \frac{1}{ \cos {}^{2} (5x) } \times 5 = \frac{15 {tg}^{2} (5x)}{ \cos {}^{2} (5x) }$

$f'( \frac{\pi}{3} ) = 15 \times \frac{ {tg}^{2} ( \frac{5\pi}{3}) }{ \cos {}^{2} ( \frac{5\pi}{3} ) } = 15 \times \frac{ {tg}^{2} ( \frac{2\pi}{3}) }{ \cos {}^{2} ( \frac{2\pi}{3} ) } = \\ = 15 \times \frac{ {( - \sqrt{3}) }^{2} }{( - \frac{1}{2}) {}^{2} } = \frac{15 \times 3}{ \frac{1}{4} } = 45 \times 4 = 180$