d/dx arcsec(x)
To find the derivative of the inverse secant function (arcsec(x)), we can use the chain rule
To find the derivative of the inverse secant function (arcsec(x)), we can use the chain rule.
Let y = arcsec(x).
The inverse secant function can be expressed as x = sec(y).
To differentiate implicitly, we take the derivative of both sides with respect to x:
d/dx(x) = d/dx(sec(y))
So, 1 = sec(y) * d/dx(y).
To find d/dx(y), we can solve for it:
d/dx(y) = 1 / sec(y)
We know that sec(y) is equal to x, so we substitute it back in:
d/dx(y) = 1 / x
Therefore, the derivative of arcsec(x) with respect to x is 1 / x.
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