Question

Qual a derivada de cos5x/sen2x?

Answer 1

lembrando que
$sen(u) ' = cos(u)* u'\\\\cos(u)' = -sen(u)*u'$

temos
$y= \frac{cos(5x)}{sen(2x)}$

usando a regra do quociente
$\boxed{ (\frac{U}{V})'= \frac{U'*V-U*V'}{V^2} }$

temos
$u = cos(5x)\\\\u'=-sen(5x)*5\\\\\\\ v=sen(2x)\\\\v'=cos(2x)*2$

colocando na regra do quociente
$y'= \frac{-5sen(5x)*sen(2x) - cos(5x)*2*cos(2x)}{[sen(5x)]^2}$