Question

Вычислите производную функции

Answer 1

$1)\; \; g(x)=3cosx\; ,\; \; \; g'(x)=-3sinx\\\\g'(-\frac{5\pi }{6})=-3sin(-\frac{5\pi }{6})=3sin(\pi -\frac{\pi }{6})=3sin\frac{\pi}{6}=3\cdot \frac{1}{2}=1,5\\\\2)\; \; g(x)=4ctgx\; ,\; \; \; g'(x)=-\frac{4}{sin^2x}\\\\g'(-\frac{2\pi }{3})=-\frac{4}{sin^2\frac{2\pi }{3}}=-\frac{4}{sin^2(\pi -\frac{\pi }{3})}=-\frac{4}{sin^2\frac{\pi}{3}}=-\frac{4}{\frac{3}{4}}=- \frac{16}{3}=-5\frac{1}{3}$