Question

найти производную функции y=sin10x+cos9x-tg2x+ctg6x

Answer 1

$(sinu)'=cosu\cdot u'\; \; \to \; \; (sin10x)'=cos10x\cdot (10x)'=cos10x\cdot 10\\\\(cosu)'=-sinu\cdot u'\; \; \to \; \; (cos\, 9x)'=-sin\, 9x\cdot (9x)'=-9cos\, 9x\\\\(tgu)'=\frac{1}{cos^2u}\cdot u'\; \; \to \; \; (tg\, 2x)'=\frac{1}{cos^22x} \cdot (2x)'=\frac{1}{cos^22x} \cdot2\\\\(ctgu)'=-\frac{1}{sin^2u}\cdot u'\; \; \to \; \; (ctg\, 6x)'=-\frac{1}{sin^26x}\cdot (6x)'=-\frac{1}{sin^26x}\cdot 6\\\\\\y=sin\, 10x+cos\, 9x-tg\, 2x+ctg\, 6x\\\\y'=10\, cos\, 10x-9\, sin\, 9x-\frac{2}{cos^22x}-\frac{6}{sin^26x}$