Computing directional derivatives with the gradient Compute the directional derivative of the following functions at the given point P in the direction of the given
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- Derivatives of vector-valued functions Differentiate the following function. r(t) = ⟨4, 3 cos 2t, 2 sin 3t⟩arrow_forwardDerivative rules Let u(t) = 2t3 i + (t2 - 1) j - 8 k and v(t) = et i + 2e-t j - e2t k. Compute the derivative of the following function. u(t) ⋅ v(t)arrow_forward[Directional Derivatives] Calculate the following directional derivatives. w(x, y, z) = xy^2 / z^2 at the point (6, 1, 2) in the direction toward (5, 2, 5).arrow_forward
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