1. The problem asks to differentiate the expression $\frac{y}{t}$ with respect to $t$. 2. We recognize this as a quotient, so we apply the quotient rule: if $f(t) = \frac{y}{t}$, then $f'(t) = \frac{t \frac{dy}{dt} - y \cdot 1}{t^2}$. 3. This gives us the derivative: $$\frac{d}{dt}\left(\frac{y}{t}\right) = \frac{t \frac{dy}{dt} - y}{t^2}$$ 4. In simpler terms, we differentiate the numerator $y$ with respect to $t$ (denoted $\frac{dy}{dt}$), multiply by $t$, subtract the product of $y$ and the derivative of the denominator $t$ (which is 1), and divide all by $t^2$. Final answer: $$\boxed{\frac{d}{dt}\left(\frac{y}{t}\right) = \frac{t \frac{dy}{dt} - y}{t^2}}$$