Find ds/dt. The equation provided is:\[ s = \frac{2t^4 - 3t}{t^3} \]The task is to find the derivative \(\frac{ds}{dt}\).### Explanation:This problem involves finding the derivative of a function \(s\) with respect to \(t\). The expression given is a fraction where the numerator is \(2t^4 - 3t\) and the denominator is \(t^3\).### Steps to Solve:1. **Simplify the Expression**: - Divide each term in the numerator by \(t^3\): - \(\frac{2t^4}{t^3} = 2t\) - \(\frac{-3t}{t^3} = -\frac{3}{t^2}\) - This simplifies the expression to: \[ s = 2t - \frac{3}{t^2} \]2. **Differentiate the Simplified Expression**: - Use the power rule \(\frac{d}{dt}[t^n] = nt^{n-1}\) to find \(\frac{ds}{dt}\): - The derivative of \(2t\) is 2. - The derivative of \(-\frac{3}{t^2}\) is: - Rewrite as \(-3t^{-2}\) - Using the power rule: \(-3(-2)t^{-3} = 6t^{-3}\)3. **Final Result**: - Combine the derivatives: \[\frac{ds}{dt} = 2 + \frac{6}{t^3}\]Hence, the derivative \(\frac{ds}{dt}\) is \(2 + \frac{6}{t^3}\).

Name: Find ds/dt. The equation provided is:\[ s = \frac{2t^4 - 3t}{t^3} \]Th
Uploaded: 2024-03-20T06:46:42.000Z
Channel: Bartleby
Description: Find ds/dt. The equation provided is:\[ s = \frac{2t^4 - 3t}{t^3} \]The task is to find the derivative \(\frac{ds}{dt}\).### Explanation:This problem involves finding the derivative of a function \(s\) with respect to \(t\). The expression given is a