Using the Quotient rule, Find dy/dx given that y = sec(x)

d[sec(x)]/dx -->d[1/cos(x)] -->( [d[1].cos(x) - d[cos(x)].1] ) / [cos(x)]^2 -->[0.cos(x) - -sin(x).1]/ [cos(x)]^2 -->sin(x)/[cos(x)]^2 -->tan(x)sec(x) <-- Final Answer