Mathematics

This is a chain rule problem disguised as a product. You have $y$ depending on $x$, which depends on $t$, so you need $\frac{dy}{dt} = \frac{dy}{dx} \cdot \frac{dx}{dt}$. The key insight is to use the product rule to find $\frac{dy}{dx}$ first, then multiply by the derivative of $x = \sqrt{t}$ with respect to $t$. Substituting $x = \sqrt{t}$ at the end will give you your final answer in terms of $t$ alone.

This is a chain rule problem disguised as a product. You have $y$ depending on $x$, which depends on $t$, so you need $\frac{dy}{dt} = \frac{dy}{dx} \cdot \frac{dx}{dt}$. The key insight is to use the product rule to find $\frac{dy}{dx}$ first, then multiply by the derivative of $x = \sqrt{t}$ with respect to $t$. Substituting $x = \sqrt{t}$ at the end will give you your final answer in terms of $t$ alone.