Question

найти производную функции

y=(sinx/xcosx)

 

 

 

 

Answer 1

Решение во вложении)

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Answer 2

$y=frac{sin x}{x cos x}=frac{tg x}{x}$

$y'=(frac{tg}{x})'=frac{(tg x)' x-tg x *(x)'}{x^2}=\\ frac{frac{1}{cos^2 x}*x-tg x *1}{x^2}=\\ frac{frac{x}{cos^2 x}-tg x}{x^2}=\\ frac{x-cos^2 xtg x}{x^2cos^2 x}=\\ frac{x-cos x sin x}{x^2cos^2 x}$