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Math Help - Chain rule

  1. #1
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    Exclamation Chain rule

    I'm not sure what is this question asking about.

    The temperature at a point(x, y) is T(x,y), measured in degrees
    Celsius, A bug crawls so that its position after t seconds is given
    by x=\sqrt{1+t}, y=2+\frac{t}{3}, where x and y are measured in centimeters. The temperature function satisfies Tx(2,3) = 4 and Ty(2,3)=3. How fast is the temperature rising on the bug’s path
    after 3 seconds?

    How can I begin with this?

    Thank you.
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  2. #2
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    Quote Originally Posted by noppawit View Post
    I'm not sure what is this question asking about.

    The temperature at a point(x, y) is T(x,y), measured in degrees
    Celsius, A bug crawls so that its position after t seconds is given
    by x=\sqrt{1+t}, y=2+\frac{t}{3}, where x and y are measured in centimeters. The temperature function satisfies Tx(2,3) = 4 and Ty(2,3)=3. How fast is the temperature rising on the bug’s path
    after 3 seconds?

    How can I begin with this?

    Thank you.
    What you're going to need is

    \frac{dT}{dt} = T_x \frac{dx}{dt} + T_y \frac{dy}{dt}
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