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

Question

jim_thompson5910 · Answer

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)

anonymous · Answer

$$secx = \frac{1}{cosx}$$ 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 $$\sec(x)\tan(x)$$