Mathematics

The key is recognizing that $\csc x = \frac{1}{\sin x}$, so you can rewrite $g(x) = (x+1)\sin x$ — transforming a quotient into a product. Once you see it as a product, the product rule becomes your natural tool, and you'll need the derivatives of both $(x+1)$ and $\sin x$. This small rewrite often makes a messy-looking problem much cleaner.

The key is recognizing that $\csc x = \frac{1}{\sin x}$, so you can rewrite $g(x) = (x+1)\sin x$ — transforming a quotient into a product. Once you see it as a product, the product rule becomes your natural tool, and you'll need the derivatives of both $(x+1)$ and $\sin x$. This small rewrite often makes a messy-looking problem much cleaner.