derivative of secx
secxtanx
The derivative of sec(x) can be found using the quotient rule of differentiation, because sec(x) can be expressed as 1/cos(x):
sec(x) = 1/cos(x)
Taking the derivative of this expression using the quotient rule, we get:
(sec(x))’ = [cos(x)(-sin(x)) – (1)(-sin(x))]/cos^2(x)
Simplifying this expression, we get:
(sec(x))’ = -sin(x)/cos^2(x)
Recalling that tan(x) = sin(x)/cos(x), we can rewrite this as:
(sec(x))’ = -tan(x)sec(x)
So, the derivative of sec(x) is equal to negative the product of tan(x) and sec(x).
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