1. **State the problem:** Differentiate the function $d=6t-\frac{4}{t}$ with respect to $t$. 2. **Recall the differentiation rules:** - The derivative of $t^n$ with respect to $t$ is $nt^{n-1}$. - The derivative of a constant times a function is the constant times the derivative of the function. - Rewrite $\frac{4}{t}$ as $4t^{-1}$ to apply the power rule. 3. **Rewrite the function:** $$d=6t - 4t^{-1}$$ 4. **Differentiate term-by-term:** - Derivative of $6t$ is $6$. - Derivative of $-4t^{-1}$ is $-4 \times (-1) t^{-2} = 4t^{-2}$. 5. **Combine the results:** $$\frac{dd}{dt} = 6 + 4t^{-2} = 6 + \frac{4}{t^2}$$ 6. **Final answer:** $$\boxed{\frac{dd}{dt} = 6 + \frac{4}{t^2}}$$