Exercise 5: Given 𝑤 = 𝑒^𝑥−𝑦 − 𝑧^2𝑦 + 𝑥
with 𝑥 = 𝑢 − 𝑣
𝑦 = 𝑢 + 𝑢^3ln(𝑣 − 1)
𝑧 = 𝑢𝑣
find the direction of maximum directional derivative of 𝑤 = 𝑤(𝑢, 𝑣) at (𝑢, 𝑣) = (1,2) and the value of said maximum derivative.
The correct answer is (-11,-9,-2)
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