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Math Help - The chain rule

  1. #1
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    The chain rule

    Suppose a moth is lying in a circle about a candle flame so that its position at time t is given by x = cost, y = sin t. Suppose that the air temperature is given by T(x, y) = x^2e^y-xy^3. Use the chain rule to find a formula for dT/dt, the rate of change of the temperature the moth feels.

    Do I just use the chain rule for composite functions for this one?
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  2. #2
    Senior Member jakncoke's Avatar
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    Re: The chain rule

    yep
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  3. #3
    Junior Member EliteAndoy's Avatar
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    Re: The chain rule

    Yup as far as I know, all you need to do is to take the derivative of the equation with respect to time, that is, you will have to treat x and y as a different variable. But yeah, all you have to do is differentiate the equation. However though, just by looking at the equation, it probably would look messy.
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  4. #4
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    Re: The chain rule

    Quote Originally Posted by apatite View Post
    Suppose a moth is lying in a circle about a candle flame so that its position at time t is given by x = cost, y = sin t. Suppose that the air temperature is given by T(x, y) = x^2e^y-xy^3. Use the chain rule to find a formula for dT/dt, the rate of change of the temperature the moth feels.

    Do I just use the chain rule for composite functions for this one?
    Use \displaystyle \begin{align*} \frac{dT}{dt} = \frac{\partial T}{\partial x}\,\frac{dx}{dt} + \frac{\partial T}{\partial y}\,\frac{dy}{dt} \end{align*}.
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