Question

Can someone check my work? I feel like Im not applying the chain rule properly:

Answer 1

I found partialz with respect to x and y, and the dx/dt and dy/dt . As far as I know I should plug them all into the formula for the chain rule right?

Answer 2

using "Pz" to denote partials because I dont know how to type it, the formula is \[\frac{ dz }{ dt } =\frac{ Pz }{ Px } * \frac{ dx }{ dt } + \frac{ Pz }{ Py } * \frac{ dy }{ dt }\]

Answer 3

I found: \[Pz/Px = y*e^y\] \[Pz/Py = xe^y\] \[dx/dt = 5\] and \[dy/dt = -2t\]

Answer 4

My answer was \[(2-t^2)* e^{2-t^2}*5+(5t)e^{2-t^2}*(-2t)\] , am I wrong in how I applied the formula, or somewhere else?