Using the chain rule, we have:
d/dx(secx) = d/dx(1/cosx) = (-1/cos^2x) * d/dx(cosx)
We can simplify d/dx(cosx) using the identity d/dx(cosx) = -sinx, so:
d/dx(secx) = (-1/cos^2x) * (-sinx) = sinx/cos^2x
Using the trigonometric identity sinx/cosx = tanx, we can simplify further to:
d/dx(secx) = tanx/cosx
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