The derivative of secx can be found using the following steps:
1. Rewrite secx in terms of sine and cosine: secx = 1/cosx
2. Apply the quotient rule for differentiation:
d/dx (1/cosx) = (-1/cos^2x) * (-sinx)
3. Simplify the expression:
d/dx (1/cosx) = sinx/cos^2x
4. Use the identity cos^2x = 1 – sin^2x to obtain an alternative expression:
d/dx (1/cosx) = sinx/(1-sin^2x)
Therefore, the derivative of secx is sinx/cos^2x = secx * tanx.
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