Derivative of sec x
To find the derivative of sec(x), we can use the quotient rule
To find the derivative of sec(x), we can use the quotient rule. The quotient rule states that for two functions f(x) and g(x), the derivative of f(x) divided by g(x) is equal to the derivative of f(x) times g(x) minus f(x) times the derivative of g(x), divided by the square of g(x).
In this case, f(x) = 1 and g(x) = cos(x). Thus, we have:
(sec(x))’ = (1)’cos(x) – 1(sin(x)) / (cos(x))^2
= 0*cos(x) – 1*sin(x) / cos^2(x)
= -sin(x) / cos^2(x)
Recall that sec(x) is equal to 1/cos(x), and we can simplify the expression further:
(sec(x))’ = -sin(x) / cos^2(x)
= -sin(x) / (1/cos^2(x))
= -sin(x)cos^2(x)
Therefore, the derivative of sec(x) is -sin(x)cos^2(x).
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