Question

derivada de cos(1/x) ?

Answer 1

regra da cadeia: y=cos(u) -> y'= -sen(u) * u'

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