Question
Assume that \( \mathrm{y}=4 \mathrm{x} \) and \( \frac{\mathrm{dx}}{\mathrm{dt}}=9 \). Find \( \frac{\mathrm{dy}}{\mathrm{dt}} \)
Ask by Gray Carter. in the United States
Feb 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( \frac{\mathrm{dy}}{\mathrm{dt}} = 36 \)
Solution
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Extra Insights
To find \( \frac{\mathrm{dy}}{\mathrm{dt}} \), we can use the chain rule. We know that \( \mathrm{y} = 4\mathrm{x} \), so we differentiate both sides with respect to \( t \): \[ \frac{\mathrm{dy}}{\mathrm{dt}} = 4 \frac{\mathrm{dx}}{\mathrm{dt}} \] Given that \( \frac{\mathrm{dx}}{\mathrm{dt}} = 9 \), we can substitute this value into the equation: \[ \frac{\mathrm{dy}}{\mathrm{dt}} = 4 \times 9 = 36 \] Thus, \( \frac{\mathrm{dy}}{\mathrm{dt}} = 36 \).
