1. **State the problem:** Differentiate the function $f(t) = 3t^2 t = 3t^3$ with respect to $t$. 2. **Recall the power rule:** The derivative of $t^n$ with respect to $t$ is $\frac{d}{dt} t^n = n t^{n-1}$. 3. **Rewrite the function:** $f(t) = 3t^3$. 4. **Apply the constant multiple rule:** The derivative of a constant times a function is the constant times the derivative of the function. 5. **Differentiate:** $$ \frac{d}{dt} 3t^3 = 3 \cdot \frac{d}{dt} t^3 = 3 \cdot 3t^{3-1} = 9t^2 $$ 6. **Final answer:** The derivative of $3t^3$ with respect to $t$ is $9t^2$.