How To Find The Derivative Of Secx: Step-By-Step Guide With Alternative Expressions

derivative of secx

secxtanx

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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