Question:
derivative of sec x
Answer:
The derivative of sec x is calculated as
d (sec x)/dx = d (1/cos x)/dx
= {d1/dx * cos x - 1 * d (cos x)/dx}/cos2 x {Apply d{f(x)/g(x)}/dx}
= {0 * cos x - 1 * (-sin x)}/cos2 x
= sin x/cos2 x
= (sin x/cos x) * (1/cos x)
= tan x * sec x
So, d (sec x)/dx = tan x * sec x
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