d sec(x)
The mathematical expression “d sec(x)” appears to be a derivative notation
The mathematical expression “d sec(x)” appears to be a derivative notation. It represents the derivative of the secant function with respect to the variable x. To find the derivative of sec(x), we can use the rules of differentiation.
The derivative of the secant function can be derived using the quotient rule, which states that for any two functions u(x) and v(x), the derivative of u(x)/v(x) is given by (v(x)u'(x) – u(x)v'(x))/[v(x)]^2.
Let’s consider the secant function, sec(x), which can be expressed as 1/cos(x). Applying the quotient rule to this expression, we have:
d(sec(x))/dx = [cos(x)(0) – (1)(-sin(x))]/[cos(x)]^2
Simplifying further, we get:
d(sec(x))/dx = sin(x)/[cos(x)]^2
Therefore, the derivative of sec(x) with respect to x is sin(x)/[cos(x)]^2.
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