Mathematics

The key is recognizing that $\sec(g(x))$ is a composite function, so the chain rule applies: you differentiate the outer function (secant) while leaving the inner function intact, then multiply by the derivative of what's inside. Remember that $\frac{d}{dx}[\sec(u)] = \sec(u)\tan(u) \cdot \frac{du}{dx}$—this trig derivative is your starting point. Once you apply the chain rule carefully, you'll get a clean formula in terms of $g(x)$ and $g'(x)$.

The key is recognizing that $\sec(g(x))$ is a composite function, so the chain rule applies: you differentiate the outer function (secant) while leaving the inner function intact, then multiply by the derivative of what's inside. Remember that $\frac{d}{dx}[\sec(u)] = \sec(u)\tan(u) \cdot \frac{du}{dx}$—this trig derivative is your starting point. Once you apply the chain rule carefully, you'll get a clean formula in terms of $g(x)$ and $g'(x)$.