To find the derivative of sec(x) with respect to x, we can use the quotient rule. The derivative of sec(x) can be written as:
d/dx(sec(x)) = d/dx(1/cos(x))
Now, applying the quotient rule, we have:
= (cos(x)(0) – 1(-sin(x))) / (cos^2(x))
= -(-sin(x)) / (cos^2(x))
= sin(x) / (cos^2(x))
Therefore, the derivative of sec(x) is equal to sin(x) / cos^2(x).
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