Question

Use the Chain Rule to find dw/dt. (Enter your answer only in terms of t.)
w = xe^(y /z), x = t^6, y = 9 - t, z = 4 + 4t

Answer 1

Take the partial derivatives for each variable and add them.
\[w = w (x, y, z)\]
\[dw/dt = (\delta w/\delta x) + (\delta w/\delta y) + (\delta w/\delta z)\]

Answer 2

Actually, that is wrong. What I meant was:
\[(dw/dt) = (\delta w/\delta x)(dx/dt) + (\delta w/\delta y)(dy/dt) + (\delta w/\delta z)(dz/dt)\]