Mathematics

This problem asks you to differentiate a trigonometric fraction—but before you dive into the quotient rule, simplify the expression first. Rewrite $\tan x$ and $\cot x$ in terms of $\sin x$ and $\cos x$, combine the fractions in the numerator and denominator, and you'll discover the expression collapses into something much cleaner, likely a single trig function or a simple multiple of one. Once simplified, the derivative becomes straightforward.

This problem asks you to differentiate a trigonometric fraction—but before you dive into the quotient rule, simplify the expression first. Rewrite $\tan x$ and $\cot x$ in terms of $\sin x$ and $\cos x$, combine the fractions in the numerator and denominator, and you'll discover the expression collapses into something much cleaner, likely a single trig function or a simple multiple of one. Once simplified, the derivative becomes straightforward.