Question

Помогите!!! Найдите производную функции (фото)

Answer 1

$f(x)=tg^5frac{3x}{5}\\(u^5)'=5u^4cdot u'; ; ,; ; u=tgfrac{3x}{5}\\f'(x)=5cdot tg^4frac{3x}{5}cdot (tgfrac{3x}{5})'=; Big[; (tgu)'=frac{1}{cos^2u}cdot u'; Big]=\\=5cdot tg^4frac{3x}{5}cdot dfrac{1}{cos^2frac{3x}{5}} cdot Big(dfrac{3x}{5}Big)'=5cdot tg^4frac{3x}{5}cdot dfrac{1}{cos^2frac{3x}{5}}cdot dfrac{3}{5}=dfrac{3cdot tg^4frac{3x}{5}}{cos^2frac{3x}{5}}$