Derivative of secant For example, let’s use our formula for taking the derivative of 1/v to take the derivative of the secant function. d d 1 d sec x = = (cos x)−1 = −(cos x)−2 (− sin x) dx dx cos x dx This is usually written in a diﬀerent fashion; there are often many diﬀerent ways of writing combinations of trigonometric functions. The standard way of writing this is: d sin x 1 sin x sec x = −(cos x)−2 (− sin x) = = · = sec x tan x. dx cos2 x cos x cos x This is the preferred form which uses the secant and tangent functions to avoid fractions and negative exponents. As you practice calculus with trigono metric functions you’ll need to be aware of equivalent ways of describing the same result. 1

Derivative of secant

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