How do I use quotient rule to show (d/dx)(sec(x)) = sec(x)tan(x)?

Answer 1

u = d/dx(sec(x))
u = d/dx(1/cos(x))
u = [(cos(x)) * d/dx(1) - (1) * d/dx(cos(x))] / [(cos(x))^2]
u = [0 - (-sin(x))] / [(cos(x))^2] = sin(x) / [(cos(x))^2]
u = (1/cos(x)) * [(sin(x)) / (cos(x))]
u = sec(x) * tan(x)

Answer 2

sec x = 1/cos x

d/dx (sec x) = sinx/cos x * 1/cos x = tan x * sec x

Answer 3

sec[x] = 1/cos[x]

d/dx sec[x] = d/dx 1/cos[x]

d/dx 1/cos[x] = sin[x] / cos^2[x]

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

d/dx 1/cos[x] = tan[x] * sec[x]

Answer 4

we know that:
secx=1/cosx ; d(secx)/dx=d(1/cosx)/dx=?
with (u/v)'=(u'v-v'u)/v^2
(dsecx)/dx=-(-sinx)/cos^2x)
=(sinx/cosx)*(1/cosx)
we know that:
tanx=sinx/cosx and secx=1/cosx
then,
(d/dx)(1/cosx)=sec(x)tan(x)

Answer 5

sec(x) => a million / cos(x) u = a million du = 0 v = cos(x) dv = -sin(x) d(u/v) => (v * du - u * dv) / v^2 => (cos(x) * 0 - a million * (-sin(x))) / cos(x)^2 => sin(x) / cos(x)^2 => (sin(x)/cos(x)) * (a million/cos(x)) => tan(x) * sec(x)