Let (x, y) = e xy and r(t) = (t 3 , 1 + t). (a) Calculate
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Let ƒ(x, y) = exy and r(t) = (t3, 1 + t).
(a) Calculate ∇ƒ and r'(t).
(b) Use the Chain Rule for Paths to calculate d/dt ƒ(r(t)).
(c) Write out the composite ƒ(r(t)) as a function of t and differentiate. Check that the result agrees with part (b).
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a We first find the partial derivatives of fx y exy af x The grad...View the full answer
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