Question

d/dx sec x = sec x tan x verify formula

Answer 1

sec(x) = 1/cos(x)


sec(x) = (cos(x))^(-1)


d/dx[sec(x)] = d/dx[(cos(x))^(-1)]


d/dx[sec(x)] = -(cos(x))^(-2)*d/dx[cos(x)]


d/dx[sec(x)] = -(cos(x))^(-2)*(-sin(x))


d/dx[sec(x)] = (sin(x))/(cos^2(x))


d/dx[sec(x)] = (sin(x))/(cos(x))*(1/cos(x))


d/dx[sec(x)] = tan(x)*sec(x)


d/dx[sec(x)] = sec(x)*tan(x)

Answer 2

\[secx = \frac{1}{cosx}\] Using the quotient rule you get \[\frac{\cos(x)(0) + (1)(sinx)}{\cos^2x}\] which can be written as \[\frac{1}{cosx}*\frac{sinx}{cosx}\] which equals \[\sec(x)\tan(x)\]