1. ## 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?

yep

3. ## 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.

4. ## Re: The chain rule

Originally Posted by apatite
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 \displaystyle \begin{align*} \frac{dT}{dt} = \frac{\partial T}{\partial x}\,\frac{dx}{dt} + \frac{\partial T}{\partial y}\,\frac{dy}{dt} \end{align*}.