ddx secx
To find the derivative of sec(x), we’ll use the quotient rule and the fact that sec(x) is equivalent to 1/cos(x)
To find the derivative of sec(x), we’ll use the quotient rule and the fact that sec(x) is equivalent to 1/cos(x).
Using the quotient rule, the derivative of sec(x), denoted as d/dx(sec(x)), is given by:
d/dx(sec(x)) = (cos(x) * d/dx(1) – 1 * d/dx(cos(x))) / (cos(x))^2
We know that d/dx(1) is 0, since 1 is a constant. Additionally, the derivative of cos(x) with respect to x is -sin(x).
Substituting these values into the equation, we have:
d/dx(sec(x)) = (cos(x) * 0 – 1 * (-sin(x))) / (cos(x))^2
= sin(x) / (cos(x))^2
To simplify further, we can rewrite sin(x) as sec(x) * cos(x) (using the identity sin(x) = 1/csc(x)):
d/dx(sec(x)) = (sec(x) * cos(x)) / (cos(x))^2
= sec(x) / cos(x)
Since sec(x) is equivalent to 1/cos(x), this simplified expression can be written as:
d/dx(sec(x)) = 1/cos(x) * 1/cos(x)
= 1/(cos(x))^2
Therefore, the derivative of sec(x) is 1/(cos(x))^2.
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