How to solve
Each path from t to z contributes its product of derivatives; add the paths.
Steps
- Find the partials z_x and z_y.
- Find x'(t) and y'(t).
- Combine: dz/dt = z_x x' + z_y y', then evaluate at t.
Example
z = xy, x = t + 1, y = t − 2. Find dz/dt at t = 3.
- dz/dt = y·1 + x·1 = x + y = 2t − 1.
- At t = 3: 5.
Answer: 5
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