The derivative of sec x can be found using the quotient rule and trigonometric identities.
Recall that sec x can be written as 1/cos x. Therefore, we have:
(sec x)’ = ((1/cos x))’
Applying the quotient rule:
((1/cos x))’ = (0*cos x – 1*(-sin x))/(cos x)^2
Simplifying:
((1/cos x))’ = -sin x/cos^2 x
Using the identity tan x = sin x/cos x:
((1/cos x))’ = -tan x/sec^2 x
Therefore, the derivative of sec x is -tan x/sec^2 x.
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