The derivative of sec(x) is sec(x) tan(x).
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negative cotangent -- dcot(x)/dx=-csc^2(x)
No. The inverse of the secant is called the arc-secant. The relation between the secant and the cosecant is similar to the relation between the sine and the cosine - they are somehow related, but they are not inverse functions. The secant is the reciprocal of the cosine (sec x = 1 / cos x). The cosecant is the reciprocal of the sine (cos x = 1 / sin x).
Derivative of 1/x 1/x = x-1 Take the derivative (-1)x(-1-1) = -x-2 = 1/x2
1/cos(x)=sec(x). sec is short for secant.
The derivative of sin(x) is cos(x).