1. The problem statement, all variables and given/known data A two-dimensional temperature field is given by the expression [tex]T=4x^2y^2+3y^3[/tex] (a) What is the magnitude and direction of the temperature gradient at the point (2,3)? (b) What is the change in temperature [tex]dT/dS[/tex] at the point (2,3) in a direction along the curve [tex]3x-4y^2=-30[/tex] passing through the point (2,3)? 2. Relevant equations [tex]T=4x^2y^2+3y^3[/tex] [tex]3x-4y^2=-30[/tex] 3. The attempt at a solution So part (a) is pretty easy. I just found the gradient and evaluated it at the given point. However, I'm stuck on part (b). I think I have to take the dot product of the gradient of T with some unit vector of that curve. However, I don't know how to formulate this dot product. I figure that I first evaluate the gradient of T at (2,3), and then get a unit vector for that curve, evaluate that result at (2,3), then take the dot product to get dT/dS. Is this correct? If so, how do I handle the RHS of the curve? Would I move it over to the LHS and then find the unit vector? Would the 30 have to be squared when finding the magnitude of the curve too? I guess I'm a little confused with how to handle the nonzero RHS.