Derivative of sec x
sec x tan x
The derivative of sec x can be found using the quotient rule of differentiation. Recall that the secant function can be written as 1/cos x, so:
(sec x)’ = [(1/cos x)’] / (1/cos x)^2
Using the chain rule and the derivative of cos x, we get:
(sec x)’ = [-sin x / cos^2 x] / (1/cos x)^2
Simplifying the expression in the numerator and the denominator, we obtain:
(sec x)’ = -sin x / cos^3 x
Therefore, the derivative of sec x is -sin x / cos^3 x.
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