d/dx(secx)
secxtanx
To find the derivative of sec(x), we can use the formula:
d/dx(sec(x)) = sec(x) tan(x)
This formula can be derived using the chain rule and the fact that sec(x) = 1/cos(x).
To see why this formula is true, we can start by writing:
sec(x) = 1/cos(x)
Taking the derivative of both sides with respect to x using the quotient rule, we get:
d/dx(sec(x)) = d/dx(1/cos(x)) = -1/cos^2(x) * (-sin(x))
Simplifying this expression, we get:
d/dx(sec(x)) = sin(x) / cos^2(x)
Recalling that tan(x) = sin(x)/cos(x), we can rewrite this expression as:
d/dx(sec(x)) = (sin(x)/cos(x)) * (1/cos(x)) = sec(x) * tan(x)
Therefore, the derivative of sec(x) is sec(x) times tan(x).
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