Derivative of secx
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 u(x) and v(x), the derivative of their quotient u(x) / v(x) is given by:
(u'(x)v(x) – v'(x)u(x)) / [v(x)]^2
In this case, u(x) is equal to 1, and v(x) is equal to cos(x). Therefore:
(u'(x)v(x) – v'(x)u(x)) / [v(x)]^2 = (0 * cos(x) – (-sin(x) * 1)) / [cos(x)]^2
Simplifying this expression further, we get:
sin(x) / [cos(x)]^2
Thus, the derivative of sec(x) is sin(x) / [cos(x)]^2.
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