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exis [7]
3 years ago
15

Let xy=1 and let dy/dt=5 Find dx/dt when x=5

Mathematics
1 answer:
madreJ [45]3 years ago
3 0
<span>So the first step is to take the derivative of xy=1. Don't forget the product chain rule!

</span>xy=1&#10;\\x=5&#10;\\y= \frac{1}{x}=\frac{1}{5}&#10;\\ &#10;\\\frac{dy}{dt}=5&#10;\\&#10;\\x\frac{dy}{dt}+y\frac{dx}{dt}=0&#10;\\&#10;\\5\times5+ \frac{1}{5} \frac{dx}{dt}=0&#10;\\&#10;\\\frac{1}{5} \frac{dx}{dt}=-25&#10;\\&#10;\\  \frac{dx}{dt}=-125&#10;<span>

</span>
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