To find the derivative of sec(x), we need to use the quotient rule in terms of sine and cosine. Recall that:
(sec x) = 1/cos(x)
Using the quotient rule, we have:
[d/dx(sec x)] = [(cos(x)d/dx(1)) – (1*d/dx(cos(x))) / cos^2(x)]
We know that d/dx(1) = 0, and that the derivative of cosine is -sin(x). Therefore, we can simplify as follows:
[d/dx(sec x)] = [-sin(x) / cos^2(x)]= -sec(x)tan(x)
So the derivative of sec(x) is -sec(x)tan(x).
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