Find the Derivative of a Vector-Value Function Given the vector-valued functions u(t)= et + e-5tj - 4tk v(t) = ti +3t²j - 2k d find (u(t). v(t)) when t = -1. dt d dt (ū - v) (−1) =

Q: Find the directional derivative of the function f(x, y) = ln(x³ + y²) at the point (1, 3) in the…

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Q: Find f'(3), where f(t) = u(t) · v(t), u(3) = (1, 2, −1), u'(3) = (8, 1, 6), and v(t) = (t, t², t³).…

A: The given functions and function values are .The aim is to find the function value .

Q: Find the second derivative of the vector-valued function r(t) = (7t + 5 sin(t))i + (4t + 5 cos(t))j…

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Q: Find the directional derivative of in the direction of the vector (1,3) at the point (-1,2)

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Q: The temperature on a cubic box [0, 4] × [0, 4] × [0, 4] (measured in meters) can be described by the…

A: Function, Tx, y, z=x2y+y2z

Q: Find the directional derivative of f(x, y, z) = −4x² + 1y² — 32² at the point (-3, 5, -5) in the…

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Q: Find f '(2), where f(t) = u(t) v(t), ū(2) = (1, 2, -1), u' (2) = (3,0, 4), and v(t) = (t, t², t³).

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